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Pricing American Options with Jumps in Asset and Volatility

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Abstract

Jump risk plays an important role in current financial markets, yet it is a risk that cannot be easily measured and hedged. We numerically evaluate American call options under stochastic volatility, stochastic interest rates and jumps in both the asset price and volatility. By employing the Method of Lines (Meyer (2015)), the option price, the early exercise boundary and the Greeks are computed as part of the solution, which makes the numerical implementation time efficient. We conduct a numerical study to gauge the impact of jumps and stochastic interest rates on American call option prices and on their free boundaries. Jumps tend to increase the values of OTM and ATM options while decreasing the value of ITM options. The option delta is affected in a similar way. The impact of jumps on the free boundary is substantial and depends on the time to maturity. Near expiry, including asset jumps lowers the free boundary and the option holder is more likely to exercise the option, whilst including asset-volatility jumps elevates the free boundary and the option holder is less likely to exercise the option. This relation reverses at the beginning of the options life. The volatility, interest rates and their volatilities have a positive impact on the free boundaries and the option holder is less likely to exercise as these parameters increase.

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  • Blessing Taruvinga & Boda Kang & Christina Sklibosios Nikitopoulos, 2018. "Pricing American Options with Jumps in Asset and Volatility," Research Paper Series 394, Quantitative Finance Research Centre, University of Technology, Sydney.
    • Handle: RePEc:uts:rpaper:394
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    Cited by:

    1. Boda Kang & Christina Nikitopoulos Sklibosios & Erik Schlogl & Blessing Taruvinga, 2019. "The Impact of Jumps on American Option Pricing: The S&P 100 Options Case," Research Paper Series 397, Quantitative Finance Research Centre, University of Technology, Sydney.

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    More about this item

    Keywords

    American options; Method of Lines; stochastic interest rate; Jumps; Greeks;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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