We present a new approach to pricing American-style derivatives that is applicable to any Markovian setting (i.e., not limited to geometric Brownian motion) for which European call option prices are readily available. By approximating the value function with an appropriately chosen interpolation function, the pricing of an American-style derivative with arbitrary payoff function is converted to...

The Black-Scholes model gives vanilla Europen call option prices as a function of the volatility. We prove Lipschitz stability in the inverse problem of determining the implied volatility, which is a function of the underlying asset, from a collection of quoted option prices with different strikes.

Computing semiparametric bounds for option prices is a widely studied pricing technique. In contrast to parametric pricing techniques, such as Monte-Carlo simulations, semiparametric pricing techniques do not require strong assumptions about the underlying asset price distribution. We extend classical results in this area in two main directions. First, we derive closed-form semiparametric bound...

In this paper, we examine the small time-to-expiry behaviour of implied volatility in models of exponential Lévy type. In the at-the-money case, it turns out that the implied volatility converges, as time-to-expiry goes to zero, to the square root of the Gaussian member of the driving Lévy process’ characteristic triplet. In particular, the limit is zero if the Lévy process has no Gaussian part...

This paper presents a model for option pricing in markets that experience financial crashes. The stochastic differential equation (SDE) of stock price dynamics is coupled to a post-crash market index. The resultant SDE is shown to have stock price and time dependent volatility. The partial differential equation (PDE) for call prices is derived using risk-neutral pricing. European call prices ar...

W present a new approach to pricing American-style derivatives that is applicable to any Markovian setting (i.e., not limited to geometric Brownian motion) for which European call-option prices are readily available. By approximating the value function with an appropriately chosen interpolation function, the pricing of an American-style derivative with arbitrary payoff function is converted to ...

This paper considered the notion of European option which is geared towards solving analytical and numerical solutions. In particular, we examined Black-Scholes closed form solution modified (MBS) partial differential equation using Crank-Nicolson finite difference method. These equations were approximated to obtain Call Put prices. The explicit price both options found accordingly. solutions c...

This paper introduces two option strategies, zero-cost collar and covered call. After calculating various performance metrics, plotting return graphs, discussing strategy performance, we show the specific differences between options strategies provide suggestions to investors. The results that these do increase overall return, but mainly due initial premium received from shorting call