Pricing Multi-strike Quanto Call Options on Multiple Assets with Stochastic Volatility, Correlation, and Exchange Rates

ArXiv ID: 2411.16617 “View on arXiv”

Authors: Unknown

Abstract

Quanto options allow the buyer to exchange the foreign currency payoff into the domestic currency at a fixed exchange rate. We investigate quanto options with multiple underlying assets valued in different foreign currencies each with a different strike price in the payoff function. We carry out a comparative performance analysis of different stochastic volatility (SV), stochastic correlation (SC), and stochastic exchange rate (SER) models to determine the best combination of these models for Monte Carlo (MC) simulation pricing. In addition, we test the performance of all model variants with constant correlation as a benchmark. We find that a combination of GARCH-Jump SV, Weibull SC, and Ornstein Uhlenbeck (OU) SER performs best. In addition, we analyze different discretization schemes and their results. In our simulations, the Milstein scheme yields the best balance between execution times and lower standard deviations of price estimates. Furthermore, we find that incorporating mean reversion into stochastic correlation and stochastic FX rate modeling is beneficial for MC simulation pricing. We improve the accuracy of our simulations by implementing antithetic variates variance reduction. Finally, we derive the correlation risk parameters Cora and Gora in our framework so that correlation hedging of quanto options can be performed.

Keywords: Quanto Options, Monte Carlo Simulation, Stochastic Volatility, Stochastic Correlation, Hedging

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 7.5/10
• Quadrant: Holy Grail
• Why: The paper employs advanced stochastic differential equations, including GARCH-Jump, Weibull, and Ornstein-Uhlenbeck processes, along with discretization schemes and Monte Carlo simulations, indicating high mathematical complexity. It demonstrates empirical rigor by using real market data (indices and FX rates) for calibration and backtesting, implementing variance reduction techniques, and deriving specific risk parameters for hedging.

  flowchart TD
    A["Research Goal<br>Price Multi-Strike Quanto Options<br>with Multiple Assets, FX, and Volatility"] --> B["Model Selection & Benchmarking<br>Stochastic Volatility vs GARCH-Jump<br>Stochastic Correlation vs Weibull<br>Stochastic FX vs Ornstein-Uhlenbeck"]
    B --> C["Simulation Setup<br>Monte Carlo Pricing<br>Milstein Discretization<br>Variance Reduction via Antithetic Variates"]
    C --> D["Computational Process<br>Simulate Asset Paths<br>Apply Quanto Payoff<br>Convert to Domestic Currency"]
    D --> E{"Model Comparison<br>Constant vs Stochastic Parameters"}
    E -->|Benchmark| F["Constant Models"]
    E -->|Optimal Combination| G["GARCH-Jump SV + Weibull SC + OU SER"]
    F & G --> H["Key Outcomes & Contributions"]
    H --> I["Optimal Pricing Model Identified<br>Balances Accuracy & Speed"]
    H --> J["Derivation of Correlation Risk Parameters<br>Cora and Gora for Hedging"]