Meridian MCPx - OTC Derivatives Pricing and Valuation Module Introduction

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OTC Derivatives Excel Template
MCPx OTC Option Calculator

Solution Features

OTC derivatives are non-standardized financial contracts customized between financial institutions and enterprises, covering forwards, swaps, options, credit derivatives, etc. Unlike exchange-traded products, OTC derivatives offer high flexibility and can be designed according to specific enterprise needs regarding payoff structures and risk exposures. They are widely used for hedging, speculation, and structured financing.

Features of the Mammoth Options OTC Derivatives Pricing and Valuation Module:

• Supports scripting language for defining complex structured products
• Supports products with underlying assets including FX, interest rates, commodities, and equity indices
• Supports pricing and valuation, as well as batch pricing and valuation
• Supports calibration of local volatility models (Dupire, Heston) using market data
• Can calculate option premium, or inversely solve for strike price or other barrier prices
• Supports GPU acceleration (including NVIDIA and Huawei), improving computational efficiency by 1000-2000 times
• Supports Excel add-in, allowing all calculation functions to be performed within Excel

System Pricing Interface:

Detailed Description of Meridian Mammoth Options OTC Derivatives Software Features

1. Supports Scripting Language for Defining Complex Structured Products

The Meridian Mammoth Options module provides a flexible scripting language interface, allowing users to quickly define complex structured option products through custom scripts. Whether it's nested options (such as Shark Fin, Range Accrual), multi-asset linked products, or innovative designs with non-standard payoff structures, the module supports intuitive programming implementation. This feature lowers the development barrier, enabling financial institutions to respond efficiently to market changes and customize personalized products that meet customer needs. For example, users can define a hybrid OTC derivative linked to FX rates and interest rates with just a few lines of script and immediately perform valuation and risk analysis.

By defining scripts, the following product structures, among others, can be supported:

• DigitalPut (Binary Put)
• DoubleNoTouch (Double No-Touch)
• TrippleRangesPut (Three-Layer Put)
• RangeAccrual (Range Accrual)
• DigitalCall (Binary Call)
• Autocallables (Auto-Callable (Monthly Observation))
• TrippleRangesCall (Three-Layer Call)
• Double Ranges (Double-Layer Structure)
• SingleTouch (Single-Touch)
• CallPutSpread (Call-Put Spread)
• AutoCall (Auto-Call)
• SharkFin (Double Shark Fin)
• DualSharkFin (Dual Direction Shark Fin)
• DiscreteDoubleNoTouchOption (EUR/USD Daily Observed Discrete Double No-Touch Option)
• DiscreteOneTouchOptionDownside (One-Touch Option - Downside)
• DiscreteOneTouchOptionUpside (One-Touch Option - Upside)
• DiscretePingPongOption (Discrete Ping Pong Option)
• SingleRangeAccrualCall (Single-Sided Call Range Accrual)
• SingleRangeAccrualPut (Single-Sided Put Range Accrual)

2. Supports Products with Underlying Assets Including FX, Interest Rates, Commodities, and Equity Indices

This module possesses broad underlying asset support capabilities, covering:

• FX rates (e.g., USD/EUR)
• Interest rates (e.g., LIBOR, SHIBOR)
• Commodities (e.g., gold, crude oil) and
• Equity indices (e.g., CSI 300, S&P 500).

This multi-asset compatibility makes the module suitable for diverse market scenarios. Whether it's FX structured deposits, commodity-linked options, or equity index-related derivatives, users can complete design, pricing, and hedging analysis on a unified platform. This flexibility is particularly suitable for institutional investors and trading teams requiring cross-asset allocation.

3. Supports Pricing and Valuation, and Supports Batch Pricing and Valuation

The pricing function calculates the theoretical price (option premium) of OTC options, while the valuation function calculates the fair value (MTM) of OTC options at a specific point in time and analyzes position risk. Supports simultaneous pricing and valuation of a large number of option contracts, with real-time aggregation and analysis.

• Batch Calculation:
  • Supports parallel processing of thousands of transactions (utilizing GPU acceleration)
  • Can group by dimensions such as counterparty, product type, underlying asset, etc.
• Real-time Aggregation and Hedging Analysis:
  • Risk Exposure Aggregation by Asset: e.g., aggregating Delta for FX options by currency.
  • Sensitivity Indicator Aggregation: Calculating net Gamma, Vega, etc., for the portfolio.
  • Hedging Suggestions: Automatically generating hedging strategies based on risk exposure (e.g., suggesting the spot quantity required to hedge Delta).

Exposure Hedging Monitoring Interface:

4. Supports Calibration of Local Volatility Models (Dupire, Heston) Using Market Data

The Meridian Mammoth Options module has built-in advanced volatility model calibration functionality, supporting the Dupire local volatility model and the Heston stochastic volatility model. Users can automatically calibrate model parameters by inputting market data (e.g., option quotes, historical volatility), ensuring pricing results are highly consistent with actual market conditions. For example, when processing FX options, the module can calibrate the mean reversion speed and volatility of volatility parameters of the Heston model using real-time FX option prices, thereby improving the valuation accuracy of complex options. This feature provides users with a scientific, data-driven pricing foundation.

The Meridian Mammoth Options module supports calibration of the Dupire local volatility model, providing high-precision pricing for FX options. The calibration process outputs include 6 parameters (e.g., -0.27958, etc.) defining the volatility surface. Model accuracy is validated via MAPE (9.42%, perfect calibration < 10%), CV-RMSE (0.0092, perfect calibration < 0.03), and Pearson correlation coefficient (0.9968, close to 1), ensuring predicted premiums highly align with market data. In-sample and out-of-sample comparisons further demonstrate the model's robustness, making it suitable for real-time valuation and risk management.

5. Supports Monte Carlo Simulation for Calculations

The module supports the Monte Carlo simulation method, efficiently handling valuation needs for path-dependent options (e.g., Asian options, range accruals) and multi-factor products. By simulating multiple possible price paths of the underlying asset, the module can accurately calculate the option's expected value and risk exposure. Users can customize the number of simulations and random seed to balance calculation accuracy and speed. For example, for a range accrual product linked to gold prices, the module can derive the payoff distribution and knockout probability through millions of path simulations, helping users optimize product design.

6. Can Calculate Option Premium, or Inversely Solve for Strike Price or Other Barrier Prices

The Meridian Mammoth Options module provides two-way calculation capabilities: it can calculate option premiums based on given strike prices, upper/lower barrier prices, and can also inversely derive corresponding strike prices or other key parameters by inputting a target option premium. This flexibility is particularly useful in product design and market quoting. For example, a bank can input the premium a client is willing to pay to inversely calculate a suitable knockout upper barrier, thereby designing more attractive structured deposits. Furthermore, the module supports multi-parameter linked adjustments, ensuring calculation results align with market expectations and risk preferences.

7. Supports Generation of Intermediate Calculation Process Reports

The module has built-in detailed report generation functionality. Users can obtain complete intermediate results and analysis reports during the calculation process. These reports include, but are not limited to, volatility surfaces, path simulation data, sensitivity analysis (Greeks), and transparent records of valuation assumptions. This feature not only facilitates internal review and risk management but also provides clients with professional and credible product explanations. For example, when generating a report for an interest-rate-linked option, users can obtain discount factors and Delta values for each step, enhancing product transparency and interpretability.

8. Supports GPU Acceleration

The Meridian Mammoth Options module fully utilizes GPU parallel computing capabilities, significantly improving the efficiency of complex calculations. For tasks requiring high computational load (such as Monte Carlo simulations, multi-asset option pricing), in batch calculation scenarios, GPU acceleration can reduce processing time from several hours to several minutes.

9. Supports Excel Add-in

All functionalities related to local volatility surface construction, option structure definition, pricing, and valuation are replicated in Excel, helping traders quickly prototype new product designs.

OTC Derivative Definition Script Functionality Description

Script Definition Overview

The script functionality of the Meridian Mammoth Options module provides users with a powerful and flexible way to define and manage the payoff logic of complex structured option products. Through an intuitive scripting language, users can define conditions, calculate payoffs, and generate cash flows at different time nodes (such as start date, observation periods, and expiry date). This functionality supports various underlying assets (e.g., FX, interest rates, commodities, equity indices) and is applicable to path-dependent products (e.g., barrier options, range accruals) as well as innovative financial derivative designs.

Core Features

• Multi-Time Node Support: Allows defining specific logic at each stage of the product lifecycle, from initialization to final payment.
• Flexible Condition Handling: Supports complex rules like knock-out, knock-in through conditional statements and mathematical operations.
• Dynamic Payoff Calculation: Integrates market data and user parameters for real-time payment amount calculation.
• Cash Flow Generation: Outputs final results via the pays instruction, compatible with Monte Carlo valuation and xVA analysis.

Syntax

The scripting language of the Meridian Mammoth Options module is based on concise syntax rules, supporting variable definition, conditional logic, mathematical operations, and payment instructions. The following describes the core syntax elements and usage.

1. Time Nodes

• Syntax: TimeNodeName (e.g., ReferenceDate, ObservationSchedule, ExpiryDate, EndDate).
• Usage: Define logic chronologically in the script, each node corresponding to a stage in the product lifecycle.
• Note: Node names must match system pre-defined or user-configured names.

2. Variable Assignment

• Syntax: VariableName = Value or VariableName = Function()
• Usage:
  • Initializing state: aLive = 1
  • Calling market data: ObservationRate = Spot()
• Note: Variable names are case-sensitive, supporting numbers, Boolean values, and function return values.

3. Conditional Statements

• Syntax:

  if (Condition) then
      Statement(s)
  else
      Statement(s)
  endif

• Usage:
  • Checking state: if (aLive = 1) then
  • Nested conditions: if (CallPutType = 0 and Spot() > Barrier) then
• Note:
  • Supports comparison operators (=, >, <, >=, <=) and logical operators (and, or).
  • Supports multi-level nesting.

4. Mathematical Operations

• Syntax: Variable = Expression
• Usage:
  • Basic operations: Yield = Spot() * 0.05 + 10
  • Function calls: Yield = max(0, Spot() - Barrier)
• Note:
  • Supports addition (+), subtraction (-), multiplication (*), division (/).
  • Built-in functions include max(), min(), Spot() (underlying price), t() (time factor).

5. Payment Instruction

• Syntax: pays Expression
• Usage:
  • Generating cash flow: pays Notional * Yield * t()
• Note: Marks the final payment; the expression result is passed as the cash flow value to the valuation engine.

Built-in Functions and Variables

• Spot(): Returns the current underlying asset price.
• t(): Returns the time factor (usually the annualized time length).
• User Variables: e.g., Barrier, Notional, ParticipateRate, need to be defined externally to the script or input via the system.

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Example

The following is a script example for a Barrier Option, demonstrating how to define payoff logic within the Meridian Mammoth Options module. The product is a call knock-out option, linked to an underlying asset (e.g., FX rate or equity index), featuring a knockout barrier and a payoff cap.

Example Script

ReferenceDate
aLive = 1                  # Product initially active
Yield = 0                  # Initial payoff rate is 0
ObservationRate = Spot()   # Record initial underlying price
CallPutType = 0            # 0 indicates call option
tt = 0                     # Time initialization

ObservationSchedule
"if (CallPutType = 0) then
    if (aLive = 1 and Spot() > Barrier) then 
        aLive = 0          # Underlying price exceeds barrier, knocks out
    endif
else
    if (aLive = 1 and Spot() < Barrier) then 
        aLive = 0          # Put option knock-out logic (not used here)
    endif
endif"

ExpiryDate
"if (aLive = 0) then 
    Yield = MidYield       # Payoff if knocked out is the mid yield
else 
    if (CallPutType = 0) then
        Yield = LowYield + (max(0, Spot() - Barrier) / ObservationRate) * ParticipateRate
    else
        Yield = LowYield + (max(0, Barrier - Spot()) / ObservationRate) * ParticipateRate
    endif
    if (Yield > HighYield) then 
        Yield = HighYield  # Cap the payoff
    endif
endif"

EndDate
opt pays Notional * Yield * t()  # Final payment amount

Parameter Description

• Barrier: Knock-out barrier price (external input, e.g., 100).
• Notional: Principal amount (external input, e.g., 10000).
• LowYield: Minimum yield (e.g., 2%).
• MidYield: Knock-out yield (e.g., 3%).
• HighYield: Maximum yield (e.g., 5%).
• ParticipateRate: Participation rate (e.g., 0.8).

Example Run Logic

1. ReferenceDate:
   • Initializes product state, records initial underlying price (e.g., Spot() = 95).
2. ObservationSchedule:
   • Daily check if Spot() exceeds Barrier (e.g., 100).
   • If on a certain day Spot() = 102, then aLive = 0, product knocks out.
3. ExpiryDate:
   • If knocked out (aLive = 0), Yield = MidYield (e.g., 3%).
   • If not knocked out and at expiry Spot() = 105:
     • Yield = 2% + (max(0, 105 - 100) / 95) * 0.8 ≈ 2.042%.
     • Check cap: If HighYield = 5%, then Yield = 2.042%.
4. EndDate:
   • Payment amount: 10000 * 0.02042 * 1 = 204.2 (assuming t() = 1).

Intermediate Calculation Process Report (Verifying Calculation Rationality and Accuracy)

The Meridian OTC Derivatives Module can generate intermediate calculation process reports for result verification, risk management, and audit purposes. Intermediate reports are divided into: Local Volatility Calibration Report and Monte Carlo Calculation Process Report.

Local Volatility Calibration Report

Detailed explanations of the intermediate calibration process and outputs can be viewed via the Excel formula HmReport(). These outputs reflect the accuracy and effectiveness of the model calibration. The explanation below will analyze the meaning of each parameter and indicator step by step to help you understand their significance in product documentation or technical reports.

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Dupire / Heston Model Calibration Intermediate Process Output Explanation

1. Basic Information

• Model: Dupire/Heston
  • Meaning: The Dupire model is a local volatility model describing volatility via a two-dimensional function of the underlying asset price and time to maturity. Unlike constant volatility models like Black-Scholes, it captures the implied volatility smile and skew of the market, making it suitable for pricing complex options (e.g., structured options).
  • The Heston model is a stochastic volatility model that introduces an independent stochastic process to describe the dynamic change of volatility, used to more accurately capture the volatility smile and skew in option markets.
• Asset Class: Forex/Commodity/Interest/Equity
  • Meaning: Calibration is targeted at the FX market, e.g., USD/CNY FX options. FX market volatility characteristics (such as exchange rate jumps, central bank intervention effects) are incorporated into the model.

2. Calibration Parameters (Dupire Model Example)

• Output: -0.27958, -0.00112442, 0.0886524, -0.000145987, 0.00399575, 0.272404
• Explanation:
  • These are the parameters obtained after calibrating the Dupire model, typically corresponding to the polynomial or spline interpolation coefficients of the local volatility function.
  • Number of Parameters: 6 parameters indicate the use of a certain parameterized form (e.g., quadratic or cubic polynomial) to fit the volatility surface.
  • Specific Meanings:
    • -0.27958: Could be the constant term, representing the baseline level of the volatility surface.
    • -0.00112442, 0.0886524: Likely related to linear terms of the underlying asset price (Spot) or time (Time-to-Maturity).
    • -0.000145987, 0.00399575, 0.272404: Could be higher-order terms (e.g., quadratic, cubic terms), capturing nonlinear changes in volatility.
  • Usage: These parameters define the local volatility function (\sigma(S, t)), used for predicting option prices and risk sensitivities (e.g., Delta, Vega).

3. Mean Absolute Percentage Error (MAPE)

• Output: 9.41953%

• Explanation:

  • Definition: MAPE measures the average relative error between the model's predicted option premiums (Predicted Premiums) and the actual market premiums (Actual Premiums). Calculation formula:

    $$\text{MAPE} = \frac{1}{n} \sum_{i=1}^n \left| \frac{\text{Actual}_i - \text{Predicted}_i}{\text{Actual}_i} \right| \times 100\%$$

  • Result Analysis:
    • 9.41953% < 10%, falls under "Perfect Calibration" (Perfect Calibration: 0-10%).
    • Indicates the model's predicted values are highly consistent with market data, with minimal error, suitable for high-precision pricing scenarios.
  • Significance: Low MAPE indicates the Dupire model captures the implied volatility structure of FX options well.

4. Coefficient of Variation of Root Mean Square Error (CV-RMSE)

• Output: 0.00920668

• Explanation:

  • Definition: CV-RMSE is the Root Mean Square Error (RMSE) divided by the mean of the actual values, measuring the relative variability of prediction errors. Formula:

    $$\text{CV-RMSE} = \frac{\sqrt{\frac{1}{n} \sum_{i=1}^n (\text{Actual}_i - \text{Predicted}_i)^2}}{\text{mean}(\text{Actual})}$$

  • Result Analysis:
    • 0.00920668 < 0.03, falls under "Perfect Calibration" (Perfect Calibration: 0-0.03).
    • Indicates the model's prediction errors are very stable with low variability.
  • Significance: Low CV-RMSE indicates high consistency of the Dupire model's predictions across different strike prices and maturities, suitable for handling the smoothness of the volatility surface.

5. Pearson Correlation Coefficient

• Output: 0.996807

• Explanation:

  • Definition: The Pearson correlation coefficient measures the linear correlation between predicted and actual values, ranging from -1 to 1. Formula:

    $$r = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum (x_i - \bar{x})^2 \sum (y_i - \bar{y})^2}}$$

    where (x_i) are predicted premiums and (y_i) are actual premiums.
  • Result Analysis:
    • 0.996807 is close to 1, indicating a very strong positive linear relationship between predicted and actual values.
    • High correlation shows the model reproduces the trend of market data well.
  • Supplementary Note:
    • The output mentions Spearman's rank correlation coefficient (more suitable for nonlinear relationships) but does not provide a specific value. The high Pearson coefficient is sufficient to prove the model's linear fitting capability.
  • Significance: High correlation enhances confidence in the model's reliability, especially in valuation and hedging.

6. Predicted vs. Actual Premium Comparison


• Output Description:
  • Y-axis: Model predicted option premiums (Predicted Premiums).
  • X-axis: Market actual option premiums (Actual Premiums).
  • Visual comparison via chart.
• Explanation:
  • Visualization Goal: Check if predicted values lie close to the 45-degree line ((y = x)).
  • Expected Result:
    • If points are densely distributed near the 45-degree line, it indicates high consistency between predictions and actual values, aligning with MAPE 9.42% and Pearson 0.9968 results.
    • If deviations exist, it may indicate volatility for certain strikes or maturities is not fully captured.
  • Significance: This chart visually verifies model calibration quality, helping users identify potential systematic bias.

7. In-Sample & Out-of-Sample Comparison


• Output Description:
  • Uses 85% of data as the training set (In-Sample) to calibrate parameters, and the remaining 15% as the test set (Out-of-Sample).
  • Chart compares predicted premiums and actual premiums.
• Explanation:
  • In-Sample:
    • Represents the model's performance on training data, typically with low error (close to MAPE 9.42%).
    • Reflects the model's fitting capability.
  • Out-of-Sample:
    • Represents the model's predictive power on new data, testing generalization performance.
    • If out-of-sample error remains below 10%, it indicates the model is not overfitting and has strong predictive power.
  • Significance:
    • Validates the model's robustness through the 85%/15% split.
    • If the chart shows similar point distributions in-sample and out-of-sample, it indicates the Dupire model has good adaptability in the FX market.

Monte Carlo Calculation Process

The Monte Carlo simulation function of the Meridian Mammoth Options module provides users with a powerful tool to assess the value and risk of complex option products. The intermediate report records key data from the simulation process in detail, helping users understand the product's potential payoff distribution and market performance. The following is an overview of the report content, demonstrating how it aids your financial decision-making.

1. Simulation Overview: Understanding Your Product Foundation

The report first presents the basic setup of the simulation, allowing you to quickly grasp the core parameters of the product. For example:

• Model & Parameters: Assuming you are designing an equity index-linked knock-out option, the report shows the use of the Heston model, start date November 18, 2024, underlying initial price 5000, risk-free rates 1.454% and 0.5%, number of simulation paths 10000, each path containing 31 observation points.
• Significance: This information ensures you understand the product's market environment and calculation scale. 10000 simulations provide high-precision results; 31-day paths are suitable for short-term structured product design.

2. Simulation Statistics: Insight into Key Path Payoff Probabilities


The core of the intermediate report is the simulation statistics section, showing the distribution of the underlying asset price at expiry, helping you predict product performance. For example:

• Data Example:
  • Average price range: 4715.59 to 5269.85.
  • Median: e.g., 4917.78 to 5292.3.
  • Volatility range: Standard deviation from 22.34 to 184.68, lowest price 4471.22, highest price 5527.57.
• Significance: These numbers provide an intuitive understanding of the possible fluctuations in the underlying price. For instance, the average price is close to the initial 5000, but the maximum 5527 and minimum 4471 indicate significant uncertainty. This is crucial for assessing knock-out probability and payoff caps. You can optimize product design by adjusting parameters (e.g., barrier level).

3. Schedule & Events: Observing Key Knock-In/Knock-Out Price Positions in Product Simulation Paths


The report includes the product's event schedule, clearly displaying the logic at each key node. For example:

• Time Range: From November 18, 2024 to December 18, 2024.
• Event Logic:
  • Daily check: If the underlying price exceeds the barrier (5300), the product knocks out.
  • Expiry calculation: If knocked out, yield is 8%; if not knocked out, calculation based on excess return, capped at 1.8%.
  • Final payment: Principal 100 million multiplied by yield and time factor (0.083).
• Significance: The schedule allows you to control product behavior throughout. For example, if designing a knock-out option, the report shows how the knock-out status is judged daily and how the payoff is automatically calculated at expiry. This transparency helps explain product rules to clients.

4. Result Output

The final results summarize the comprehensive performance of the simulation, providing an intuitive value assessment. For example:

• Example Results:
  • Survival probability: 87.77% (proportion of non-knocked-out paths).
  • Average yield: 0.836976%.
  • Option value: 69,552 CNY.
• Significance: These indicators provide a basis for your pricing and sales strategy. An 87.77% survival rate indicates a low knock-out probability. The yield of 0.836976%, although lower than the maximum 1.8%, is much lower than the knock-out yield of 8%, reflecting the product's risk-return balance. The option value of 69,552 CNY can serve as a reference for quoting, directly supporting your market decisions.

The Monte Carlo simulation intermediate report of the Meridian Mammoth Options module is not just a calculation tool but also a powerful assistant for designing and promoting your products. From parameter setting to statistical analysis, to event tracking and result output, each part provides you with clear market insights and decision support. Whether optimizing product structure or demonstrating value to clients, this report can help you achieve more with less effort.