The Financial Greeks

The Financial Greeks

Introduction

Options are commonly used by financial institutions, professionals as well as the astute private investor to reduce the volatilities in their investment portfolio returns and in so doing, achieve a certain sense of predictability. An in-depth understanding concerning the parameters of interest, namely delta, gamma, vega, theta and rho, in no order of precedence, is therefore essential for the formulation of any viable hedging strategy, commensurate with the terms of investment risk returns.

Individual Greeks

A) Delta

The put call parity example illustrated in an article (Jay, 2001) that is based on the binomial options valuation model i.e. only 2 possible outcomes of underlying asset price can be used to derive the value of the call or put option. Usage of binomial methods are highly presumptuous as the asset price has theoretically unlimited outcomes by the time of exercising the corresponding option which implies that the concept of probability of each potential outcome should be considered i.e. Black- Scholes options valuation model in the pricing of said option. Option delta which represents the correlation between the changes in the option price and the change in the underlying asset is therefore used for both models to determine the valuation of the option as well as a delta neutral portfolio. The value of a call option is simply the option delta multiplied by the share price and deducting the bank loan i.e. continuously compounded or the rate free interest rate for the Black- Scholes and binomial valuation models respectively (Jay, 2001). In essence, a small increase in the price of an underlying asset for instance, is hedged by the reciprocal of the delta in the concurrent holding of a corresponding call option. The reverse is true for a put option relating to a decrease in the price of a corresponding asset for example. Delta changes with time to option expiration and the values of 1 and 0 are commensurate...