At maturity, a powered call option pays off max(S - X, 0)^i and a put pays off max(X - S, 0)^i . Esser (2003 describes how to value these options (see also Jarrow and Turnbull, 1996, Brockhaus, Ferraris, Gallus, Long, Martin, and Overhaus, 1999). (via "The Complete Guide to Option Pricing Formulas") b=r options on non-dividend paying stock b=r-q options on...
Power options can lead to very high leverage and thus entail potentially very large losses for short positions in these options. It is therefore common to cap the payoff. The maximum payoff is set to some predefined level C. The payoff at maturity for a capped power call is min . Esser (2003) gives the closed-form solution: (via "The Complete Guide to Option...
Library "cbnd" Description: A standalone Cumulative Bivariate Normal Distribution (CBND) functions that do not require any external libraries. This includes 3 different CBND calculations: Drezner(1978), Drezner and Wesolowsky (1990), and Genz (2004) Comments: The standardized cumulative normal distribution function returns the probability that one random...
Sprenkle 1964 Option Pricing Model w/ Num. Greeks is an adaptation of the Sprenkle 1964 Option Pricing Model in Pine Script. The following information is an except from Espen Gaarder Haug's book "Option Pricing Formulas". The Sprenkle Model Sprenkle (1964) assumed the stock price was log-normally distributed and thus that the asset price followed a geometric...