Pricing American Options With Jumps in Asset and Volatility

41 Pages Posted: 17 Nov 2018

See all articles by Blessing Taruvinga

Blessing Taruvinga

University of Technology Sydney (UTS), UTS Business School, Finance Discipline Group

Boda Kang

AMP

Christina Sklibosios Nikitopoulos

University of Technology Sydney - Business School; Financial Research Network (FIRN)

Date Written: October 24, 2018

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.

Keywords: American Options, Method of Lines, Stochastic Interest Rate, Jumps, Greeks

JEL Classification: C60, G13

Suggested Citation

Taruvinga, Blessing and Kang, Boda and Sklibosios Nikitopoulos, Christina, Pricing American Options With Jumps in Asset and Volatility (October 24, 2018). Available at SSRN: https://ssrn.com/abstract=3272506 or http://dx.doi.org/10.2139/ssrn.3272506

Blessing Taruvinga (Contact Author)

University of Technology Sydney (UTS), UTS Business School, Finance Discipline Group ( email )

15 Broadway, Ultimo
PO Box 123
Sydney, NSW 2007
Australia

Boda Kang

AMP ( email )

Sydney, NSW
Australia
0430976988 (Phone)
2154 (Fax)

Christina Sklibosios Nikitopoulos

University of Technology Sydney - Business School ( email )

15 Broadway, Ultimo
Sydney 2007, New South Wales
Australia

Financial Research Network (FIRN)

C/- University of Queensland Business School
St Lucia, 4071 Brisbane
Queensland
Australia

HOME PAGE: http://www.firn.org.au

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