We analyze the regularity of the optimal exercise boundary for the American Put option when the underlying asset pays a discrete dividend at a known time td during the lifetime of the option. The ex-dividend asset price process is assumed to follow Black-Scholes dynamics and the dividend amount is a deterministic function of the ex-dividend asset price just before the dividend date. The solutio...

In this paper we review several relationships between prices of put and call options, of both the European and the American type, obtained mainly through Girsanov Theorem, when the asset price is driven by a time-changed Lévy process. This relation is called put-call duality, and includes the relation known as put-call symmetry as a particular case. Necessary and sufficient conditions for put-c...

Since Black and Scholes published their seminal paper [2] in 1973, the pricing of options by means of deterministic partial differential equations or inequalities has become standard practise in computational finance. An option gives the right (but not the obligation) to buy (call option) or sell (put option) a share for a certain value (the exercise price K) at a certain time T (exercise date)...

The stock market is a popular topic in Twitter. The number of tweets concerning a stock varies over days, and sometimes exhibits a significant spike. In this paper, we investigate the relationship between Twitter volume spikes and stock options pricing. We start with the underlying assumption of the Black–Scholes model, the most widely used model for stock options pricing, and investigate when ...

We introduce options on FTSE100 index in portfolio optimisation with shares in which conditional value at risk (CVaR) is minimised. The option considered here is the one that follows FTSE100 Index Option standards. Price of options are calculated under the risk neutral valuation. The efficient portfolio composed under this addition of options shows that put option will be selected as part of th...

This paper studies an optimal stopping time problem for pricing perpetual American put options in a regime switching model. An explicit optimal stopping rule and the corresponding value function in a closed form are obtained using the “modified smooth fit” technique. The solution is then compared with the numerical results obtained via a dynamic programming approach and also with a two-point bo...

This paper is devoted to the valuation of American multi-asset put options. It is well known that the American multi-asset put option satisfies a linear complementary problem (LCP) on an unbounded domain. We consider a penalty method in which the LCP could be reformulated into a nonlinear parabolic problem on an unbounded domain. For the unbounded computational domain, a perfectly matched layer...

One of the most widely studied problems in financial mathematics is the pricing of derivative securities, also known as contingent claims. These are securities whose price depend on the value of another underlying security. Financial options are the most common examples of derivative securities. For example, a European call option on a particular underlying security gives the holder the right t...