The oil company holds the investment opportunity to develop a delineated oilfield. The investment plan must be presented until a specific date or the oilfield rights return to the government. The firm considers a set of mutually exclusive alternatives of scale to exploit the oilfield. Larger scale means faster exploitation – increasing the present value of revenues, but also higher investment c...

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...

The article concerns the generalised Cox‑Ross‑Rubinstein (CRR) op­tion pricing model with new formulas for changes in upper and lower stock prices. formula option this model, which is Black‑Scholes type formula, its asymptotics are presented. aim of paper to analyse limiting cases obtained as­ymptotics using probability theory later data from Warsaw Stock Exchange. Empirical analyses gener­alis...

We call a given American option representable if there exists European claim which dominates the payoff at any time and such that values of two options coincide in continuation region option. This concept has interesting implications from probabilistic, analytic, financial, numeric point view. Relying on methods (Math. Finance 24 (2014) 156–172; Ann. Inst. H. Poincaré Anal. Non Linéaire 18 (200...

This paper solves the dynamic investment problem of a risk averse manager compensated with a call option on the assets he controls. Under the manager’s optimal policy, the option ends up either deep in or deep out of the money. As the asset value goes to zero, volatility goes to infinity. However, the option compensation does not strictly lead to greater risk seeking. Sometimes, the manager’s o...

The objective of this paper is twofold. Firstly, to derive time-fractional evolution equation modeling the No-Arbitrage premium Asian option (with arithmetic and geometric averages ) contingent upon an underlying asset that satisfies fractional stochastic differential equation, in a setting when strike price fixed floating. Secondly, we have computed four versions put-call parities for options,...

Several researchers have proposed modeling temporally abstract actions in reinforcement learning by the combination of a policy and a termination condition, which we refer to as an ”option”. Value functions over options and models of options can be learned using methods designed for semi-Markov decision processes (SMDPs). However, these methods all require an option to be executed to terminatio...

Forecasting volatility is important to financial asset pricing because a more accurate forecast will allow for a more accurate model to price financial assets. Currently the VIX is used as a measure of volatility in the market as a whole, but a major issue with this is that it is calculated based on manually traded options on the S&P 500. Another method of forecasting volatility is that of solv...

This paper shows how the prices of option contracts traded in financial markets can be tracked sequentially by means of the Extended Kalman Filter algorithm. I consider call and put option pairs with identical strike price and time of maturity as a two output nonlinear system. The Black-Scholes approach popular in Finance literature and the Radial Basis Functions neural network are used in mode...

Given the price of a call or put option, the Black-Scholes implied volatility is the unique volatility parameter for which the Bulack-Scholes formula recovers the option price. This article surveys research activity relating to three theoretical questions: First, does implied volatility admit a probabilistic interpretation? Second, how does implied volatility behave as a function of strike and ...