Implied Volatility in Merton’s Jump Diffusion Model

The “implied volatility” corresponding to an option price is the value of the volatility parameter for which the Black-Scholes model gives the same price. A well-known phenomenon in market option prices is the “volatility smile”, in which the implied volatility increases for strike values away from the spot price. The jump diffusion model is a generalization of Black\[Dash]Scholes in which the stock price has randomly occurring jumps in addition to the random walk behavior. One of the interesting properties of this model is that it displays the volatility smile effect. In this Demonstration, we explore the Black-Scholes implied volatility of option prices (equal for both put and call options) in the jump diffusion model. The implied volatility is modeled as a function of the ratio of option strike price to spot price.


About Jonathan

Dr Jonathan Kinlay is the founder and CEO of Systematic Strategies, LLC, a systematic hedge fund that deploys high frequency trading strategies using news-based algorithms. Dr Kinlay is also the founder and CEO of Algorithmic Execution, LLC, a New-York based broker dealer specializing in algorithmic trading solutions for high frequency trading firms. Dr Kinlay, was the founder and General Partner of the Caissa Capital hedge fund, whose volatility arbitrage strategies were developed by Dr Kinlay's investment research firm, Investment Analytics. Caissa, which managed $400M in assets, was ranked by FIMAT as the top performing fund in its class in 2004. Dr Kinlay went on to establish the Proteom Capital, whose statistical arbitrage strategies were based on pattern recognition techniques used in DNA sequencing. Dr Kinlay was formerly Global Head of Model Review at the US investment bank Bear Stearns. Dr Kinlay holds a PhD in economics and has held positions on the faculty at New York University Stern School of Business, Carnegie Mellon and Reading Universities. Dr Kinlay is a regular conference speaker and writer on investment research, hedge fund investing and quantitative finance. Dr Kinlay was a member of England's chess team that won gold in the World Student Olympiad in Mexico in 1978. He is the son of Fleet Street editor James Kinlay and father of British actress Antonia Kinlay.
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