Ebook Options, futures, and other derivatives (10/E): Part 2
➤ Gửi thông báo lỗi ⚠️ Báo cáo tài liệu vi phạmNội dung chi tiết: Ebook Options, futures, and other derivatives (10/E): Part 2
Ebook Options, futures, and other derivatives (10/E): Part 2
www.downloadslide.netThe Greek LettersA financial institution that sells an option to a client in the over-the-counter markets is faced with the probl Ebook Options, futures, and other derivatives (10/E): Part 2lem 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 ol' a client and does Ebook Options, futures, and other derivatives (10/E): Part 2not correspond to the standardized products traded by exchanges, hedging the exposure is far more difficult.In this chapter we discuss some of the altEbook Options, futures, and other derivatives (10/E): Part 2
ernative approaches to this problem. We cover what arc commonly referred to as the "Greek letters", or simply the "Greeks". Each Greek letter measureswww.downloadslide.netThe Greek LettersA financial institution that sells an option to a client in the over-the-counter markets is faced with the probl Ebook Options, futures, and other derivatives (10/E): Part 2s presented in this chapter IS applicable to market makers in options on an exchange as well as to traders working in lhe over-the-counter market for financial institutions.Toward the end of the chapter, we w ill consider the creation of options synthetically. Tin’s turns out to be very closely rela Ebook Options, futures, and other derivatives (10/E): Part 2ted to the hedging of options. Creating an option position synthetically is essentially the same task as hedging the opposite option position. Eor exaEbook Options, futures, and other derivatives (10/E): Part 2
mple, creating a long call option synthetically is the same as hedging a short position in the call option.19.1ILLUSTRATIONin the next few sections wewww.downloadslide.netThe Greek LettersA financial institution that sells an option to a client in the over-the-counter markets is faced with the probl Ebook Options, futures, and other derivatives (10/E): Part 2g 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 (0.3846 years), and the expected return from the stock is 13% per annum.1 With our usual notation, this Ebook Options, futures, and other derivatives (10/E): Part 2means thatSo = 49. A = 50. r = 0.05, Ơ = 0.20. T = 0.3846. M=0.13The Black Scholes Merton price of the option is about S24O.OOO. (This is because the'Ebook Options, futures, and other derivatives (10/E): Part 2
As shown in Chapters 13 and 15, the expected return is irrelevant to the pricing of an option. It is given here because it can have some bearing on twww.downloadslide.netThe Greek LettersA financial institution that sells an option to a client in the over-the-counter markets is faced with the probl Ebook Options, futures, and other derivatives (10/E): Part 2has therefore sold a product for S60.000 more than its theoretical value. But it is faced with the problem of hedging the risks."19.2NAKED AND COVERED POSITIONSOne strategy open to the financial institution is to do nothing. This is sometimes referred to as a naked position. Il is a strategy that wo Ebook Options, futures, and other derivatives (10/E): Part 2rks well if the stock price is below $50 al the end of the 20 weeks, rhe option then costs the financial institution nothing and it makes a profit ofEbook Options, futures, and other derivatives (10/E): Part 2
$300,000. A naked position works less well if the call is exercised because the financial institution then has Io buy 100.000 shares at the market priwww.downloadslide.netThe Greek LettersA financial institution that sells an option to a client in the over-the-counter markets is faced with the probl Ebook Options, futures, and other derivatives (10/E): Part 2trike price. For example, if after 20 weeks the stock price is $60. the option costs the financial institution SI.000.000. This is considerably greater than the $300,000 charged for the option.As an alternative to a naked position, the financial instilulion can adopt a covered position. This involve Ebook Options, futures, and other derivatives (10/E): Part 2s buying 100.000 shares as soon as the option has been sold. II' the option is exercised, this strategy works well, but in other circumstances It coulEbook Options, futures, and other derivatives (10/E): Part 2
d lead to a significant loss. For example, if the slock price drops lo S40. the financial institution loses $900,000 on its slock position. Tills is awww.downloadslide.netThe Greek LettersA financial institution that sells an option to a client in the over-the-counter markets is faced with the probl Ebook Options, futures, and other derivatives (10/E): Part 2ptions underlying the Black Scholes Menon formula hold, the cost to the financial institution should always be $240,000 on average for both approaches.1 But on any one occasion the cost is liable lo range from zero Io over SI.000,000. A good hedge would ensure that the cost IS always close to $240,0 Ebook Options, futures, and other derivatives (10/E): Part 200.A Stop-Loss StrategyOne interesting hedging procedure that is sometimes proposed involves a stop-loss strategy. To illustrate the basic idea, consiEbook Options, futures, and other derivatives (10/E): Part 2
der an institution that has written a call option with strike price K to buy one unit of a stock. The hedging procedure involves buying one unit of thwww.downloadslide.netThe Greek LettersA financial institution that sells an option to a client in the over-the-counter markets is faced with the probl Ebook Options, futures, and other derivatives (10/E): Part 2lock price is less than K and a covered position whenever the stock price is greater than K. The procedure is designed Io ensure that al lime 7' the institution owns the slock if the option closes in I he money and does not own it if the option closes out of the money. In the situation illustrated i Ebook Options, futures, and other derivatives (10/E): Part 2n Figure 19.1. it involves buying the stock at time f|, selling It at time i2. buying it al time h, selling it al time u, buying it at time ty, and deEbook Options, futures, and other derivatives (10/E): Part 2
livering it at lime T.A call option on a non-dividend-paving stock is a convenient example with which to develop our ideas. The points that wilt be mawww.downloadslide.netThe Greek LettersA financial institution that sells an option to a client in the over-the-counter markets is faced with the probl Ebook Options, futures, and other derivatives (10/E): Part 2osure from writing a naked put' More precisely, the present value of the expected cost is $240,000 for both approaches assuming that appropriate risk-adjusted discount rates arc usedwww.downloadslide.netThe Greek Letter!,399As usual, we denote the initial stock price by £|. The cost of setting up th Ebook Options, futures, and other derivatives (10/E): Part 2e hedge initially is 5|) if 5|| K and zero otherwise. It seems as though the total cost. Q, of writing and hedging the option is the option's inilialEbook Options, futures, and other derivatives (10/E): Part 2
intrinsic value:Q = max(S) - K. 0)-19.1This is because all purchases and sales subsequent to lime 0 are made al price K. II’ ihis were in fact correctwww.downloadslide.netThe Greek LettersA financial institution that sells an option to a client in the over-the-counter markets is faced with the probl Ebook Options, futures, and other derivatives (10/E): Part 2n its Black Scholes Merton price, thus, a trader could cam riskless profits by writing options and hedging them.Ihcrc arc two key reasons why equation (19.1) is incorrect, rhe first is that the cash flows to lhe hedger occur at dilĩerent times and must be discounted. The second is that purchases and Ebook Options, futures, and other derivatives (10/E): Part 2 sales cannot be made al exactly the same price K. This second point is critical. If we assume a risk-neutral world with zero interest rates, we can jEbook Options, futures, and other derivatives (10/E): Part 2
ustify ignoring the lime value of money. But we cannot legitimately assume that both purchases and sales are made at the same price. If markets are efwww.downloadslide.netThe Greek LettersA financial institution that sells an option to a client in the over-the-counter markets is faced with the probl Ebook Options, futures, and other derivatives (10/E): Part 2e at a price K + c and sales must be made at a price K - c. for some small positive number c. Thus, every' purchase and subsequent sale involves a cost (apart from transaction crisis) of If-. A natural response on the part of the hedger is to monitor price movements mote closely, so that f is reduce Ebook Options, futures, and other derivatives (10/E): Part 2d. Assuming that stock prices change continuously, e can be made arbitrarily small by monitoring the slock prices closely. But as f is made smaller, tEbook Options, futures, and other derivatives (10/E): Part 2
rades tend to occur more frequently. Thus, the lower cost per trade is offset by the increased frequency of trading. Ast-* 0. the expected number of twww.downloadslide.netThe Greek LettersA financial institution that sells an option to a client in the over-the-counter markets is faced with the probl Ebook Options, futures, and other derivatives (10/E): Part 2al is infinite.www.downloadslide.net400CHAPTER 19www.downloadslide.netThe Greek LettersA financial institution that sells an option to a client in the over-the-counter markets is faced with the problGọi ngay
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