Closed form option pricing formulae explaining skew and smile are obtained within a parsimonious non-Gaussian framework. We extend the non-Gaussian option pricing model of L. Borland (Quantitative Finance, 2, 415-431, 2002) to include volatility-stock correlations consistent with the leverage effect. A generalized Black-Scholes partial differential equation for this model is obtained, together ...

European Range Accrual Option pricing and deviation Formula has been deduced through observing the foundational asset probabilistic distribution characteristics with help of Ito’s lemma, relaxing boundary assumption to infinity zero respectively, classical Black-Scholes option formula worked out. This paper subsequently articulates numerical value simulated computation algorithm using...

Nonlinear Black–Scholes equations have been increasingly attracting interest over the last two decades, since they provide more accurate values by taking into account more realistic assumptions, such as transaction costs, risks from an unprotected portfolio, large investor’s preferences or illiquid markets, which may have an impact on the stock price, the volatility, the drift and the option pr...

American options are different to European style options in that the contract buyer has the right to exercise the option at any time on or before maturity . The freedom to exercise an American option whenever the holder wishes, introduces a boundary problem to solving the Black-Scholes equation popularly used to price the European options. The contract holder will ideally, of course, only exerc...