Mathematics of the Financial Markets: Financial Instruments and Derivatives Modelling, Valuation and Risk Issues

10

Option pricing in general

10.1 INTRODUCTION TO OPTION PRICING

An option is a contract granting:

• the right to its holder, the option buyer – but the obligation to its issuer, the seller,
• to negotiate, that is, either to buy (call option) or to sell (put option), if the option buyer exercises its right,
• at a price, fixed in advance and called the exercise price or strike price some quantity of underlying instrument (stock, currency, bond, etc.),
• at a given maturity date or until a given maturity date: in the first case, one refers to a European option, in the second, to an American option.

To some extent, this definition reminds us of an insurance contract. The insured party (the option buyer) pays an insurance premium to the insurer (the option seller), to be insured against something that could happen, and in this instance, exercises its right to be indemnified according to the contract clauses. The insurance premium is perceived by the insurer in any case, and must be sized so that the indemnification requests – that represent some probabilistic outcome – are compensated by the sum of insurance premiums. In the case of options, since the option buyer would exercise its option if such exercise implies a profit – that is, a loss for the option seller – the option seller is entitled to perceive an option premium, in the same way as the insurer.

For the beginner, dealing with options may be a source of confusion, since the human brain is mostly used to consider binary situation ...