“In order to make any progress, it is necessary to think of approximate techniques, and
above all, numerical algorithms... Once again, what became a major endeavor of mine, the …

The pressure to reduce inventory has increased as competition expands, product variety
grows, and capital costs increase. This investigation addresses the problem of inventory …

Valuing and hedging derivatives consistent with the volatility smile has been a major
research focus for over a decade. A breakthrough occurred in the mid-nineties with the …

The current method employed by the Johannesburg Stock Exchange 1 (JSE) to determine
implied volatility is based on trade data and a linear deterministic approach. The aim of this …

A forward equation, which is also called the Dupire formula, is obtained for European call
options when the price dynamics of the underlying risky assets are assumed to follow a …

We explore the pricing of compound derivatives under the newly introduced conjugate-
power Dagum distribution. Assuming a discrete-time multiplicative conjugate-power Dagum …

The simple compound option model has many limitations when applied in practice. The
research on compound option theory mainly focuses on two directions. One is the extension …

The exchange traded index option market in South Africa has seen tremendous growth
during the last couple of years. The biggest liquidity is in options on the near and middle Alsi …

In this paper, the call option price is evaluated based on linear investment strategy in order
to hedge the risk actively in stock market with stochastic interest rate. The Vasicek model is …

We derive forward partial integrodifferential equations (PIDEs) for pricing up-and-out and
down-and-out call options when the underlying is a jump diffusion. We assume that the jump …