On the Approximation of the Black and Scholes Call Function
Giuseppe Orlando and Giovanni Taglialatela, On the approximation of the Black and Scholes call function, Journal of Computational and Applied Mathematics, 28 August 2020, https://www.sciencedirect.com/science/article/abs/pii/S0377042720304453
Posted: 9 Nov 2020
Date Written: August 28, 2020
The Black and Scholes call function is widely used for pricing and hedging. In this paper we present a new global approximating formula for the Black and Scholes call function that can be useful for deriving the risk of options i.e. the implied volatility. Lastly we compare, by numerical test, our results with some popular methods available in literature (which are generally local) and we show, through Monte Carlo analysis, the computation error for extreme cases of both volatility and moneyness.
Keywords: Black and Scholes model, Hyperbolic tangent, Implied volatility, Inverse problem
JEL Classification: G10, C02, C88
Suggested Citation: Suggested Citation