Certain exotic options cannot be valued using closed-form solutions or even by numerical methods assuming constant volatility. Many exotics are priced in a local volatility framework. Pricing under local volatility has become a field of extensive research in finance, and various models are...

Hedging down-and-out puts (and up-and-out calls), where the maximum payoff is reached just before a barrier is hit that would render the claim worthless afterwards, is challenging. All hedging methods potentially lead to large errors when the underlying is already close to the barrier and the...

We address a number of technical problems with the popular Practitioner Black-Scholes (PBS) method for valuing options. The method amounts to a two-stage procedure in which fitted values of implied volatilities (IV) from a linear regression are plugged into the Black-Scholes formula to obtain...

VaR (Value at Risk) and CVaR (Conditional Value at Risk) are implied by option prices. Their relationships to option prices are derived initially under the pricing measure. It does not require assumptions about the distribution of portfolio returns. The effects of changes of measure are modest...

This paper examines a simple basis risk model based on correlated geometric Brownian motions. We apply quadratic criteria to minimize basis risk and hedge in an optimal manner. Initially, we derive the Föllmer–Schweizer decomposition for a European claim. This allows pricing and hedging under...

In this paper we formulate the Risk Management Control problem in the interest rate area as a constrained stochastic portfolio optimization problem. The utility that we use can be any continuous function and based on the viscosity theory, the unique solution of the problem is guaranteed. The...

A contingent claims valuation model which allows to highlight the implications of program trading in spot markets for the pricing of European-style foreign currency options and for the volatility strike structure implicit in these contracts is devoloped. The curvature of the volatility strike...

The effectiveness of the foreign exchange market interventions conducted by the Deutsche Bundesbank during the Louvre period to alter either the level or the volatility of the $/DM spot rate is examined. Volatility quotes implicit in foreign currency options are employed to recover the impact of...

The main objective of this paper is to present an algorithm of pricing perpetual American put options with asset-dependent discounting. The value function of such an instrument can be described as VωAPut(s)=supτ∈TEs[e−∫0τω(Sw)dw(K−Sτ)+], where T is a family of stopping times, ω is...

In this paper, the pricing performances of two learning networks, namely an artificial neural network and a bootstrap aggregating ensemble network, were compared when pricing the Johannesburg Stock Exchange (JSE) Top 40 European call options in a modern option pricing framework using a...