Finance II 2007: Derivatives Peter Chingoma
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Objective Test 1: Solutions Section A
(12 Marks)
1) You have purchased a call option that expires immediately if the market price of the underlying security falls below a specified price. This type of option is known as a (n) ….. a) Asian option b) Barrier option c) Lookback option d) Binary 2) A call option has a delta of 0.5. If the share price rises, holding all else constant, the delta will….. a) It is impossible to tell with the given information. b) Decrease. c) Remain constant. d) Increase. 3) American call options written on shares are more valuable than European call options written on the same underlying asset with the same time to maturity and exercise price. This situation is…. a) Never true b) Always true c) Always true for dividend paying shares d) Sometimes true for dividend paying shares 4) Which of the following does not affect the value of an option? a) Risk free interest rate. b) Share price c) Expected return on the share d) Volatility of share returns 5) The one year risk free rate is 10%. A put and call option with the same exercise price have the same market price. The time to maturity is 1 year for both options. Given that the stock price is R50, what is the exercise price of the options? a) R50 b) R52.50 c) R55 d) R57.50 6) Which of the following statements is not necessarily true? Holding all else constant….. a) Increasing the risk free rate increases the value of the call option. b) Increasing the volatility of returns of the underlying asset increases the
Finance II 2007: Derivatives Peter Chingoma
[email protected]
value of a call option c) Increasing the price of the underlying asset increases the value of a call option. d) Lowering the exercise price of a call option increases the value of the option. Section B 1.
2. b) d1 is 0.210084 and d2 is -0.15734
[2]
a) N(d1) is 0.583199 and N(d2) is0.437489.
[2]
b) R7.01 (use put call-parity)
[3]
c) Delta of call option is same as N(d1)
[1]
3. A Binary option is an exotic option which pays a fixed amount if the share price is above a certain level at maturity or zero otherwise. [2] Section C First we calculate the market values of the three bonds: 0.5 year bond: R1000e-0.5 x 0.0925 = R954.80
[1]
1-year bond: R1000e-1 x 0.0944 = R909.92
[1]
1.5 year bond: R1000e-1.5 x 0.0956 = R866.41
[1]
Finance II 2007: Derivatives Peter Chingoma
[email protected]
The total value of our portfolio is thus: R954.80 + 909.92 + R866.41 = R2731.13 The duration for the bonds is simply their maturity periods since we’re working with a NACC rate. [1] The mean change in value is then: (954.80 x 0.0056 x -0.5) + (909.92 x 0.0077 x -1) + (866.41 x 0.0082 x -1.5) = -2.67344 – 7.0064 – 10.66 = -20.34 [2] The variance is: (954.8 x -0.5 x 0.0046)2 + (909.92 x -1 x 0.0062)2 + (866.41 x -1.5 x 0.0074)2 + (2 x 954.8 x 909.92 x -0.5 x -1 x 0.0046 x 0.0062 x 0.86) + (2 x 909.92 x 866.41 x -1 x -1.5 x 0.0062 x 0.0074 x 0.89) + (2 x 954.8 x 866.41 x -0.5 x -1.5 x 0.0046 x 0.0074 x 0.81) = 4.82259 + 31.83 + 92.50 + 21.31 + 108.51 + 96.57 + 34.21 = 281.23 Therefore the standard deviation is: 16.77
[3]
The one-month 95% VaR is thus: -20.34 – 1.645 x 16.77 = R47.93 or 1.75% of our portfolio value of R2731.13 [1] Section D (Bonus marks)
(5 marks)
1. The put call parity theorem will not hold because the American put can be exercised early. The American call on a non dividend paying share is the same as a European Call option. Since the American put can be exercised early the put and call will not have the same times to maturity and hence put-call parity will not hold. [2] 2. Write the put, short sell a share, buy the call option and lend the present value of the exercise price(buy a zero coupon bond with face value equal to the exercise price) [3]