EXOTIC POWER QUANTO OPTION VALUATION WITH STOCHASTIC VOLATILITY, JUMP RISK, AND LONG-RANGE DEPENDENCE

Abstract

This study suggests a comprehensive model to price exotic power quanto options that have stochastic volatility, long memory, jumps and long memory. This is necessitated by the inadequacy of conventional pricing models that tend to assume constant volatility, continuous price movement, and short memory returns, which are not likely to be the case with nonlinear cross-currency derivatives. The combined model is characterized by a power payoff and a quanto in a domestic risk-neutral setting, and the foreign underlying position is exposed to time-varying volatility jumps, and long-range dependence through a fractional component. Since there are no closed-form solutions to the problems of such complexity, the paper applies the Monte Carlo method to price options and compare with simpler models, including the Black-Scholes and hybrid pricing models.

The results prove that the composite model gives bigger option prices that are more real as compared to the benchmark models and thus reduced-form models might be underestimating such options. The findings also indicate that jump risk, volatility dynamics, maturity, the Hurst exponent, and the power coefficient have a strong influence when it comes to option prices. The study contributes to the exotics option pricing literature by providing a more realistic and flexible model to value and manage risks of complex quanto-linked derivatives.