Spring 2022
Using our understanding of Black-Scholes model the goal is determining a way to price power options and finding a closed-form solution to price these exotic derivatives.
Power options are a class of exotic options in which the payoff at expiry is related to the $n^{th}$ power of the stock price, where $n = 1,2,...$ . For a power option on a stock with price $S_t$ having a strike price K and time to expiry , the payoff is $max(S_{T}^n - K, 0)$ for a call, and $max(K - S_{T}^n, 0)$ for a put. Within the Black-Scholes model, closed-form solutions exist for the price of power options. In this demonstration, prices as function of the various parameters are explored.
For a given asset the call/put of a power option would be computed via:
Ethereum Power option payoff
Bitcoin Power option payoff
