Like we established in the introductory article, an option represents a right with no obligations for the option holder. Also, we saw that the seller of an option runs a much greater risk than the buyer, which is why a premium passes from buyer to seller. To liken it to our everyday lives, we can observe that the valuations the options seller must make are comparable to the considerations an insurance company makes when pricing an insurance policy - the two parties have to agree on the size of the premium. This is where it gets challenging, so let's have a look at the considerations that must be made.

We can start by establishing that the premium can never be negative, since payoff at maturity is zero or positive. Digging deeper, the size of the premium must naturally depend on the choice of strike, the time to maturity and the expected movements in the underlying FX rate. However, the price of options also has much to do with our abilities to replicate the payoff.

Starting off very simply, if we choose to buy a call option and sell a put option with the same strike and maturity we end up with a payout profile at maturity equal to that of a long FX forward outright contract, with a difference attributable to funding cost on the option premium which is paid up front (see Figure 1). So a call option can always be replicated by the comparable put option combined with a forward contract and vice versa.

This relationship is known as the put-call parity. Given the price of an equivalent option, it is possible to replicate the payoff thereby inducing a price on the option being valued. Replication using the underlying forward or spot is the main cornerstone used to price options and is the foundation of the famous Black-Scholes pricing formula. The Black-Scholes model and its extension to FX markets, the German-Kohlhagen model, is based on trading the underlying. We will not go into the details about this here, but we will look into it in upcoming articles regarding hedging. Great intuition can, however, be made of the Black-Scholes model and the general pricing of options. The Black-Scholes model prices the option using strike, spot, time to maturity, interest rates of the domestic and foreign currencies in the underlying, and finally volatility.

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