Jump models vs crash models for the valuation of options in environments high volatility
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This paper carries out a comparative analysis between the models of jumps and crashes taking as reference the basic solution from Black-Scholes-Merton (BSM) (1973). The main results are that, in an environment of high volatility, the BSM model excessively overvalues the price of European call options. Although the crash model shows an improvement in the valuation, the jump model provides more adequate premiums. That is to say, the jump model is a better alternative for option pricing in an environment of high volatility.
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This paper carries out a comparative analysis between the models of jumps and crashes taking as reference the basic solution from Black-Scholes-Merton (BSM) (1973). The main results are that, in an environment of high volatility, the BSM model excessively overvalues the price of European call options. Although the crash model shows an improvement in the valuation, the jump model provides more adequate premiums. That is to say, the jump model is a better alternative for option pricing in an environment of high volatility.