This paper develops a general stochastic model of a frictionless security market with continuous trading. The vector price process is given by a semimartingale of a certain clr;zss, and the general stochastic integral is used to represent capital gains. Within the framework of this model, we discuss the modern theory of contingent claim valuation, including the celebrated option pricing formula...

This paper discusses the generalized Black-Scholes-Merton model, where volatility coefficient, drift coefficient of stocks, and interest rate are time-dependent deterministic functions. Together with it, we make assumption that volatility, drift, depend on a gamma or inverse-gamma random variable. model includes models skew Student’s t- variance-gamma-distributed stock log-returns. The price Eu...

We compute a sharp small-time estimate for the price of a basket call under a bi-variate SABR model with both β parameters equal to 1 and three correlation parameters, which extends the work of Bayer,Friz&Laurence[BFL14] for the multivariate Black-Scholes flat vol model. The result follows from the heat kernel on hyperbolic space for n = 3 combined with the Bellaiche[Bel81] heat kernel expansio...

In modern finance, the value of an active investment strategy is measured by comparing its performance against the benchmark of passively holding the market portfolio and the riskless asset. We wish to evaluate the marginal contribution of a theoretical derivatives pricing model in the same way, by comparing its performance against an "informationally passive" alternative model. All rationally ...

Financial derivatives have grown in importance over the last 40 years with futures and options being actively traded on a daily basis throughout world. The need to accurately price such financial instruments has, thus, also increased, which has given rise several mathematical models among is that of Black, Scholes, Merton whose wide acceptance partly justified by its ability mature well-develop...

This paper investigates Black–Scholes call and put option thetas, and derives upper and lower bounds for thetas as a function of underlying asset value. It is well known that the maximum time premium of an option occurs when the underlying asset value equals the exercise price. However, we show that the maximum option theta does not occur at that point, but instead occurs when the asset value i...