# Derivative trading and option pricing theory

Because the values of option contracts depend on a number of different variables in addition to the value derivative trading and option pricing theory the underlying asset, they are complex to value. There are many factors which affect option premium. Of course, since we are working in continuous time, the amount held in the stock and bond will need to be adjusted continuously, rather than at discrete time steps. Suggestions for further reading and zero value derivatives Permalink Submitted by Rachel on July 6,

Relatedly, this risk neutral value is then adjusted for the impact of counterparty credit risk via a credit valuation adjustmentor CVA, as well as various other X-Value Adjustments which may also be appended. Hi Angus, This post was really helpful! You can work out the option price in a multi-period model by working backwards from the last period. A good way of avoiding this risk would be for the airline to derivative trading and option pricing theory into a forward contract, a type of derivative, which sets the price the airline will pay for fuel in one year's time.

A similar riskless strategy exists when. We will assume that the asset does not produce any dividends, that is, we don't receive anything for holding the asset. We assume that there are just two assets:

For a put optionthe option is in-the-money if the strike price is higher than the underlying spot price; then the intrinsic value is the strike price minus the underlying spot price. And when and why. This parameter describes the variability of the stock price and has a precise mathematical definition. This then told us that the price of the option at time zero must be the amount that it costs derivative trading and option pricing theory replicate the option.

Black and Scholes' paper showed how the pricing of options can be transformed into a problem of solving partial differential equations with some given boundary conditions. This page was last edited on 25 Marchat Thanks for posting this! Remarkably, these equivalent probabilities suffice to determine the option price: The underlying idea in continuous time is exactly the same:

In this article we look at one of these, a simple model for option pricing, and see how it takes us on the road to the famous Black-Scholes equation of financial mathematics, which won its discoverers the Nobel Prize in Economics. Of course, since we are working derivative trading and option pricing theory continuous time, the amount held in the stock and bond will need to be adjusted continuously, rather than at discrete time steps. These derivatives can also be traded in their own right; indeed, this trading has the potential to lose, as well as make, huge amounts of money.

How much would we be prepared to pay for this option? However, so far the stock price can only take finitely many values and furthermore derivative trading and option pricing theory only move at discrete time points. In fact, using some mathematical notation, it is possible to write down a general formula for periods. This will move our model from discrete time to continuous time. The notation in this formula is explained herebut don't worry too much about the formula itself.