tailieunhanh - Ebook Options, futures, and other derivatives (10/E): Part 2
(BQ) Part 2 book “Options, futures, and other derivatives” has contents: The greek letters, volatility smiles, basic numerical procedures, credit derivatives, estimating volatilities and correlations, real options, equilibrium models of the short rate, and other contents. | 19 The Greek Letters C H A P T E R A financial institution that sells an option to a client in the over-the-counter markets is faced with the problem of managing its risk. If the option happens to be the same as one that is traded actively on an exchange or in the OTC market, the financial institution can neutralize its exposure by buying the same option as it has sold. But when the option has been tailored to the needs of a client and does not correspond to the standardized products traded by exchanges, hedging the exposure is far more difficult. In this chapter we discuss some of the alternative approaches to this problem. We cover what are commonly referred to as the ‘‘Greek letters’’, or simply the ‘‘Greeks’’. Each Greek letter measures a different dimension to the risk in an option position and the aim of a trader is to manage the Greeks so that all risks are acceptable. The analysis presented in this chapter is applicable to market makers in options on an exchange as well as to traders working in the over-the-counter market for financial institutions. Toward the end of the chapter, we will consider the creation of options synthetically. This turns out to be very closely related to the hedging of options. Creating an option position synthetically is essentially the same task as hedging the opposite option position. For example, creating a long call option synthetically is the same as hedging a short position in the call option. ILLUSTRATION In the next few sections we use as an example the position of a financial institution that has sold for $300,000 a European call option on 100,000 shares of a non-dividendpaying stock. We assume that the stock price is $49, the strike price is $50, the risk-free interest rate is 5% per annum, the stock price volatility is 20% per annum, the time to maturity is 20 weeks ( years), and the expected return from the stock is 13% per With our usual notation, this means that S0 ¼ 49; K ¼ .
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