Abstract We present closed-form solutions to the problems of pricing perpetual American double lookback put and call options on maximum drawdown drawup with floating strikes in Black-Merton-Scholes model. It is shown that optimal exercise times are first at which underlying risky asset price process reaches some lower or upper stochastic boundaries depending current values its running minimum a...

In this paper, the pricing of a European call option on the underlying asset is performed by using a Monte Carlo method, one of the powerful simulation methods, where the price development of the asset is simulated and value of the claim is computed in terms of an expected value. The proposed approach, applied in Monte Carlo simulation, is based on the Black-Scholes equation which generally def...

Upper and lower hard bounds of the expected value on stochastic differential equations can be obtained with the help of the mathematical programming and the Dynkin formula, without recourse to Monte Carlo sample paths simulation. In this paper, we show that feasible solutions of those optimization approaches further provide useful additional information. Namely, feasible solutions provide upper...

We propose a new cognitive framework for option price modelling, using quantum neural computation formalism. Briefly, when we apply a classical nonlinear neuralnetwork learning to a linear quantum Schrödinger equation, as a result we get a nonlinear Schrödinger equation (NLS), performing as a quantum stochastic filter. In this paper, we present a bidirectional quantum associative memory model f...

This paper considers the pricing of discretely sampled Asian and lookback options with ̄oating and ®xed strikes. In the modelling framework of Black and Scholes (1973), it is shown that a change of numeraire of the martingale measure can be used to reduce the dimension of these path-dependent option pricing problems to one in addition time. This means that the pricing problems can be solved by n...

A course has been developed to learn computational methods from the web and has been tested with postgraduate students from remote universities. Short video conferences or video recordings provide an overview and introduce more detailed studies with numerical experiments in Java-powered course notes. This enables every participant to work at his own pace and to develop his intuition for finite ...

A warrant is a derivative that gives the right, but not obligation, to buy or sell security at certain price before expiration. The valuation method was inspired by option because of similarities between these two derivatives. formula under Black–Scholes available in literature. However, known have number flaws; hence, this study aims develop pricing for warrants incorporating jumps, stochastic...

We study the numerical approximation of viscosity solutions for Parabolic Integro-Differential Equations (PIDE). Similar models arise in option pricing, to generalize the Black–Scholes equation, when the processes which generate the underlying stock returns may contain both a continuous part and jumps. Due to the non-local nature of the integral term, unconditionally stable implicit difference ...