Derivatives in Plain Words by Frederic Lau, with a ... - HKU Libraries

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Volatility is the most important factor in option pricing. Unlike otherfactors, the actual volatility is not known (or cannot be observed) at thetime of the option transaction. In our real estate option example, the10 percent or 30 percent volatility level is based on historical data. Itis not the actual volatility, because the actual volatility is not observableat the time of the option transaction. In option language, vega is theamount of change of an option price with one-percent change in thevolatility of the underlying.3. The option time periodThis is also obvious. The longer the option time period, the higher theoption premium (for both calls and puts). This is what we call time valueof an option. This factor is on the side of option writers. If all things remainconstant, the time value of the option decreases every day and eventuallydecreases to zero at maturity. For at-the-money or out-of-the-money options,because the intrinsic value is zero, the option becomes worthless at maturity.For in-the-money options, because there is some intrinsic value left atmaturity, the option holders can still exercise the option to purchase theunderlying asset at a price better than the market price. Therefore, it is stillworth something. An option value changes due to changes in time toexpiration. This is called theta and is always referred to as time decay.4. The level of interest ratesThe higher the interest rate, the higher the call option premium. This is notso obvious and an example is needed to illustrate this point. If I want tobuy a property or a financial asset and I am given the chance of delaying thepayment, I will, as I consider myself a rational investor, put the money in abank to earn some interest in this period. This will partially offset mypremium expense and I am willing to pay a higher premium. Therefore, forcall (put) options, the higher the interest rate the bank pays me on mydeposit, the higher (lower) the option premium I am willing to pay. Rho isthe amount of change in an option value due to changes in interest rates.In pricing financial options, market participants usually use the real interestrate or the risk-free interest rate.Introduction of Options
Three of these four factors (actually there are five elements involved - thedifference between the market price and the exercise price includes twoelements) are known at the time of the option transaction: risk-free interestrate, exercise price and the level of the asset price, and the option timeperiod. The volatility, however, has to be estimated, or based on somehistorical data. Market participants usually use implied volatility to priceoptions. (Implied volatility is the volatility level for the underlying that theoption price implies. It is a reverse process because the option price isobservable but the volatility is not.) Assuming that the seller and I haveagreed on all of these five factors, the option premium can be calculated byusing an option formula, such as the Black-Scholes formula. This process isjust a matter of mathematics. We will introduce the Black-Scholes formulain the next chapter.The following table summarises the factors of option pricing we just discussed:Premium ofCallPutHigher strike price lower higherHigher volatility higher higherLonger option time period higher higherHigher risk-free interest rate higher lowerFor stock options, there is one more factor which affects the value of anoption - dividend. Right after a company pays its stock dividend, its shareprice usually drops by an amount reflecting the dividend paid adjusting forthe tax effect (stock price may go down somewhat less than the dividendamount because of the tax effect). Therefore, dividends can be interpretedas the reduction in share prices and thus reduce the value of calls andincrease the value of puts.Introduction of Options
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THE UNIVERSITY OF HONG KONGLIBRARIE
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VI- . .7 « i8^p ! ««^^OOSHSlVCJ
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Ever since derivatives took centre-
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denominator, value at risk, which c
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the kind of information that superv
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This book is a team effort of the H
Page 14 and 15: While most market participants defi
Page 16 and 17: of this investment is 6.32 percent
Page 18 and 19: Mathematically, the relation betwee
Page 20 and 21: $10,000. (For simplification of pre
Page 22 and 23: Hong Kong does go up and the HSI ri
Page 24 and 25: 3OF ATHEPRICING OF A FORWARD CONTRA
Page 26 and 27: COST OF CARRYIn the above example,
Page 28 and 29: interest rate swap rates. From thes
Page 30 and 31: Borrowers, on the other hand, usual
Page 32 and 33: Again we use our method of having t
Page 34 and 35: ates, the forward rate for the peri
Page 36 and 37: 5In this chapter, we will discuss w
Page 38 and 39: often complain that there is too mu
Page 40 and 41: ABC also has three cash flows:1. It
Page 42 and 43: Assuming that there is no transacti
Page 44 and 45: simulation techniques and mathemati
Page 46 and 47: The calculation of credit risk proc
Page 48 and 49: The payments are exchanged every th
Page 50 and 51: the reference rate. When this type
Page 52 and 53: Effectively this is just a 2-year s
Page 54 and 55: This measure of duration is referre
Page 56 and 57: analysis, it also has its shortcomi
Page 58 and 59: Percentage change in price due to d
Page 60 and 61: 8OFOptions are generally perceived
Page 62 and 63: OPTION'S PAYOFF PATTERNWhat about a
Page 66 and 67: fANDTrading options becomes more po
Page 68 and 69: You need to hold 7 shares of stock
Page 70 and 71: di = [ln(IOO/IOO) + (0.06 + O.P/2)
Page 72 and 73: is10In the previous chapter, we dis
Page 74 and 75: stock will go up in the near future
Page 76 and 77: If the stock price of A continues t
Page 78 and 79: OF AN11In the previous two chapters
Page 80 and 81: at-the-money option approaches its
Page 82 and 83: 12Mortgage-backed securities (MBS)
Page 84 and 85: NEGATIVE CONVEXITYFor MBS, there is
Page 86 and 87: MULTI-CLASSIn 1983, Freddie Mac int
Page 88 and 89: 13What is a hedge? According to the
Page 90 and 91: management to enter into swap and o
Page 92 and 93: transaction. For this criterion to
Page 94 and 95: CREDIT DEFAULT SWAPThe simplest for
Page 96 and 97: APPLICATION OF CREDIT DERIVATIVESYo
Page 98 and 99: in the US. Equally innovative, cred
Page 100 and 101: THE VARIANCE-COVARIANCE METHODThe t
Page 102 and 103: "cell" would have a cash flow expos
Page 104 and 105: Daily profit and loss ranked in asc
Page 106 and 107: of the market factor. Through this
Page 108 and 109: 3. Most value at risk models use hi
Page 110 and 111: 16ANDIn Chapter 5, we talked about
Page 112 and 113: price) of 9,000. For this transacti
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and the June 3-month futures rate i
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needs to take the necessary busines
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ief, the policies and procedures sh
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The derivatives industry can be com
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ANDONOFINTRODUCTION1. The Monetary
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MANAGEMENT AND CORPORATE5. As the B
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ensure that there is sufficient awa
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15. Branches of foreign banks which
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20. Where the institution considers
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RISK MEASUREMENT25. Having identifi
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) the tendency of the relevant mark
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38. The measurement of the market r
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market, credit and liquidity risk o
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Consideration must be given to the
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55. As noted earlier, the market or
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changes in portfolio value;d) the r
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66. A basic and essential safeguard
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73. It is essential that the intern
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Market liquidity risk is the risk t
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Furthermore, contracts with the sam
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There are three main VAR approaches
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Options risk should be captured; ri
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Annex D1. NOTIONAL OR VOLUME LIMITS
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assumptions on which they are based
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* There should be a unit independen
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- the customer had specifically req
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addition and deletion of operators,
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• Profits and losses resulting fr
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This book is due for return or rene
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