Distribution of Returns from Merton's Jump Diffusion Model
 In the jump diffusion model, the stock price  follows the random process  . The first two terms are familiar from the Black–Scholes model: drift rate  , volatility  , and random walk (Wiener process)  . The last term represents the jumps:  is the jump size as a multiple of stock price, while  is the number of jump events that have occurred up to time  .  is assumed to follow the Poisson process  , where  is the average frequency with which jumps occur. The jump size follows a log-normal distribution  , where  is the standard normal distribution,  is the average jump size, and  is the volatility of jump size. Snapshot 1: when there are no jumps, the jump diffusion model reduces to the Black–Scholes model, in which returns follow a normal distribution Snapshot 2: the effect of jumps can be observed clearly by "turning down" the volatility of the diffusive component to zero   "Distribution of Returns from Merton's Jump Diffusion Model" from The Wolfram Demonstrations Project http://demonstrations.wolfram.com/DistributionOfReturnsFromMertonsJumpDiffusionModel/ Contributed by: Peter Falloon | ||||||||||||||
 | ||
 |
|
|
Browse all topics
