Option Pricing with Markov-Switching Stochastic Volatility and Co-Jumps

Summary

This paper develops option-pricing methods for a discrete-time model combining Markov-switching stochastic volatility with co-jumps. The model is designed to represent volatility clustering and changes in volatility’s mean-reversion speed. For European options, the authors efficiently compute the probability distribution of average integrated variance, a quantity used in pricing under stochastic volatility.

The approach extends to American-style options by recasting their pricing as the valuation of a portfolio of European options. The authors also discuss implications for variance-linked derivatives, including variance swaps. Numerical results are described as efficient and accurate, but the document provides no quantitative error measures, benchmark comparisons, or implementation details. The claims therefore summarize computational results without enough information here to assess performance across parameter settings or market conditions.

Key ideas

• The model combines stochastic volatility, Markov regime changes, and co-jumps in discrete time.
• It is designed to capture volatility clustering and changing volatility mean-reversion speeds.
• European option pricing uses the computed distribution of average integrated variance.
• American-style option pricing is transformed into valuation of a portfolio of European options.
• The methods are also relevant to variance-based derivatives, though quantitative benchmark details are not provided.

Tags

# Option Pricing Under a Discrete-Time Markov Switching Stochastic Volatility with Co-Jump Model


# Option Pricing Under a Discrete-Time Markov Switching Stochastic Volatility with Co-Jump Model









We consider option pricing using a discrete-time Markov switching stochastic volatility with co-jump model, which can model volatility clustering and varying mean-reversion speeds of volatility. For pricing European options, we develop a computationally efficient method for obtaining the probability distribution of average integrated variance (AIV), which is key to option pricing under stochastic-volatility-type models. Building upon the efficiency of the European option pricing approach, we are able to price an American-style option, by converting its pricing into the pricing of a portfolio of European options. Our work also provides constructive guidance for analyzing derivatives based on variance, e.g., the variance swap. Numerical results indicate our methods can be implemented very efficiently and accurately.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.