Abstract
We derive the Laplace transforms for the prices and deltas of the powered call and put options, as well as for the price and delta of the capped powered call option under a general framework. These Laplace transforms are expressed in terms of the transform of the underlying asset price at maturity. For any model that can derive the transform of the underlying asset price, we can obtain the Laplace transforms for the prices and deltas of the powered options and the capped powered call option. The prices and deltas of the powered options and the capped powered call option can be computed by numerical inversion of the Laplace transforms. Models to which our method can be applied include the geometric Lévy model, the regime-switching model, the Black–Scholes–Vasiček model, and Heston’s stochastic volatility model, which are commonly used for pricing of financial derivatives. In this paper, numerical examples are presented for all four models.
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