The Black-Scholes Model for pricing options is the most widely used but is not the only model. The recent vote in the UK to leave the European Union resulted in a large bump in volatility and substantial price moves, especially in the Bonds and related products (eg. TLT) which “jumped up”. Some may have wondered why the TOS platform (designed by some key members of tastytrade) and our studies, projections etc. stick with the Black-Scholes model under such circumstances. Why don't we use, for instance, the Jump Diffusion Model? Tom Preston, aka TP, our expert in options modeling, joins the guys to explain things.
Jump Diffusion pricing models are enhancements to Black-Scholes that allow discontinuous price behavior (jumps). The model contains a “jump” part that follows a Poisson distribution and factors in large, unpredictable changes in the stock price, and a “diffusion” part that has the stock moving according to Brownian Motion. The formula was displayed and TP explained it.
Using historical data the jump part inputs the average number of jumps expected between now and expiration and also the amount of the underlyings volatility that is represented by the jumps. This increases the option’s theoretical risk premium. A table of the Theoretical prices of 1 Standard Deviation 45 days to expiration (DTE) out-of-the-money (OTM) options in the SPY (S&P 500 ETF) and the TLT (Bond ETF) was displayed. The table compared the Black Scholes pricing on these options to the Jump Diffusion pricing of the options. TP discussed the table and pointed out that there is a problem with subjectivity. That is because of how much extra risk premium the jump diffusion option has is dependent upon each person’s interpretation of the frequency and magnitude of potential jumps.
Watch this segment of The Skinny On Options Modeling with Tom Sosnoff, Tony Battista and Tom Preston (TP) for the key takeaways and a better understanding of Jump Diffusion model and its comparison to the Black Scholes model in the pricing of options.
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