Title Derivatives - Solution.pdf ✅

CFA Program Level I for February 2024 1 Derivatives (Solution) 1. A. Incorrect. The value of a European call option is directly related to the price of the underlying. B. Incorrect. The value of a European call option is directly related to the volatility of the underlying. C. Correct. The value of a European call option is directly related to time to expiration. That is, all else held equal, the value of a European call option is higher the longer the time to expiration. Derivatives: identify the factors that determine the value of an option and describe how each factor affects the value of an option 2. A. Incorrect because the value of a European put option is directly related to the exercise price. Also, the value of a European put option can be either directly or inversely related to the time to expiration. The direct effect is more common. Option 1 and Option 2 have the same exercise price, but Option 2 has a longer time to expiration. So, Option 2 is more likely to have a higher value than Option 1. Option 2 and Option 3 have the same time to expiration, but Option 3 has a higher exercise price. So. Option 3 is most likely to have a higher value than Option 2. B. Incorrect because the value of a European put option is directly related to the exercise price. Also, The value of a European put option can be either directly or inversely related to the time to expiration. The direct effect is more common. Option 1 and Option 2 have the same exercise price, but Option 2 has a longer time to expiration. So, Option 2 is more likely to have a higher value than Option 1. Option 2 and Option 3 have the same time to expiration, but Option 3 has a higher exercise price. So, Option 3 is most likely to have a higher value than Option 2. C. Correct because the value of a European put option is directly related to the exercise price. Also, The value of a put option can be either directly or inversely related to the time to expiration. The direct effect is more Option 1 and Option 2 have the same exercise price, but Option 2 has a longer time to expiration. So, Option 2 is more likely to have a higher value than Option 1. Option 2 and Option 3 have the same time to, but Option 3 has a higher exercise price. So. Option 3 is most likely to have a higher value than Option 2 Derivatives: identify the factors that determine the value of an option and describe how each factor affects the value of an option 3. A. Incorrect because "the value of a European put is inversely related to the risk-free interest rate." B. Correct because "the value of a European put option is directly related to the exercise price." C. Incorrect because "the value of a European put option is inversely related to the value of the underlying."
CFA Program Level I for February 2024 2 Derivatives: identify the factors that determine the value of an option and describe how each factor affects the value of an option 4. A. Correct because -cT=-Max(0.ST-X) (payoff to the call seller), where- cT is the call value at expiration for the call seller, ST is the price of the underlying at expiration, and X is the strike price. Therefore, the Correct calculation yields: -$5=-Max(0,$30 - $25). B. Incorrect because the call value at expiration for a call seller (-cT) is not-Max(0, ST-X) + Co. where ST, is the price of the underlying at expiration, X is the strike price, and co is the option premium. Therefore, the incorrect calculation yields: $0=-Max(0, $30-$25) + $5, which is the profit for the call option seller. C. Incorrect because the call value at expiration for a call seller (-cT) is not Max(0,ST-X) + Co. where S, is the price of the underlying at expiration, X is the strike price, and co, is the option premium. Therefore, the incorrect calculation yields: $10 Max(0, $30 - $25) + $5. Instead, the correct formula is –cT= -Max(0.ST-X) (payoff [value] to the call seller), which yields: -$5=- Max(0,$30-$25) Derivatives: determine the value at expiration and profit from a long or a short position in a call or put option 5. A. Correct because S0+p0=c0 + X/(1+r)T . This relationship is known as put-call parity. Here S0, is the spot price, Po is the put premium, X is the strike price and ris the interest rate. S0 + p0 = c0+X/(1+r)T 40+ p0= 10+ 60/1.03 p0= 10+60/1.03-40 =28.25242718 = 28.25 B. Incorrect because S0+p0=c0 + X/(1+r)T .This relationship is known as put-call parity. In this response, X was not divided by (1+r)T . Here S, is the spot price, p0 is the put premium, X is the strike price and r is the interest rate. S0 + p0=c0+X/(1+r) 40+ po= 10 +60 p0= 10+60-40=30.00 C. Incorrect because S0+p0=c0 + X/(1+r)T . This relationship is known as put-call parity. In this response, S0 was incorrectly added instead of subtracted from c0 + X/(1+r)T to arrive at P0. Here S0 is the spot price. P0 is the put premium, X is the strike price and r is the interest rate. S0 + p0 = c0+X/(1+r)T
CFA Program Level I for February 2024 3 40+ p0= 10 +60 / 1.03 p0= 10+60/1.03 +40 = 108.252427 = 108.25. Derivatives: explain put-call parity for European options 6. A. Incorrect because it calculates the equivalent zero rate as: Z2 = (100-DF2)/2; or (100-96)/2 = 2.0000% Z3=(100-DF3)/3; or = (100-93)/3 = 2.3333% Accordingly, (1.020000)2 x (1 + IFR2,1)1 = (1.023333)3 (1 + IFR2,1) = (1.023333)3 /(1.020000)2 (1+IFR2,1)= (1.071646/1.04040) 1+IFR2+= 1.030033 IFR2,1= 1.030033-1=3.0033%≈ 3.00%. B. Correct because a discount factor may also be interpreted as the price of a zero-coupon cash flow or bond. The price equivalent of a zero rate is the present value of a currency unit on a future date, known as a discount factor. The discount factor for period i (DFi) is: DFi= 1/(1+zi). Accordingly, the equivalent zero rate is: DF2=0.96=1/(1+z2)2; and z2 = 2.0621% DF3 = 0.93=1/(1+z3)3; and z3 = 2.4485% The implied forward rate between period A and period B is denoted as IFRA,B-A It is a forward rate on a bond that starts in period A and ends in period B a general formula for the relationship between the two spot rates (ZA, ZB) and the implied forward rate (IFRA,B-A): (1+ZA) A × (1+ IFRA,B-A) B-A = (1 + ZB) B (1.020621)2 x (1 + IFR2,3-2)3-2= (1.024485)3 (1+IFR2,1)= (1.024485)3 /(1.020621)2 (1+IFR2,1) = (1.075269/1.041667) 1+IFR2,1 = 1.032258 IFR2,1 = 1.032258-13.2258% ≈3.23%. C. Incorrect because the implied forward rate is calculated as follows: DF2=0.96=1/(1+z2)2, and z2 = 2.0621% DF3 = 0.93=1/(1+ z3) 3 ; and z3 = 2.4485%
CFA Program Level I for February 2024 4 Accordingly, IFR2,1= (1.024485)3- (1.020621)2 IFR2,1= (1.075269 - 1.041667) IFR2,1 = 0.033602 = 3.3602% ~~ 3.36% Derivatives: Explain how forward rates are determined for interest rate forward contracts and describe the uses of these forward rates. 7. A. Incorrect because according to put-call parity. P0=c0 – S0+X/(1+r)T , long put = long call, short asset, long bond. Therefore, the payoff of a European put option is not equal to a payoff of a portfolio consisting of a long asset, a short call and a long risk-free bond. B. Correct because according to put-call parity. P0=c0 – S0+X/(1+r)T , long put = long call, short asset, long bond. Therefore, the payoff of a European put option is equal to a payoff of a portfolio consisting of a short asset, a long call and a long risk-free bond. C. Incorrect because according to put-call parity. P0=c0 – S0+X/(1+r)T long put = long call, short asset, long bond. Therefore, the payoff of a European put option is not equal to a payoff of a portfolio consisting of a short asset, a short call and a short risk-free bond. Derivatives: explain put-call parity for European options 8. A. Correct because a long put and a short call are equivalent to a long risk-free bond and short forward position: p0 –c0=[X-F0(T)](1+r)-T as calculated below: p0 –c0=[X-F0(T)](1+r)-T (4) Rearranging for c0 p0 –c0=[X-F0(T)](1+r)-T p0 = put = £4 X = exercise price = £47 F0(T) = forward = £50 r = risk-free rate = 10% p0 –c0=[X-F0(T)](1+r)-T = c0 Thus, c0 = £4-[£47-£50](1.10)-075 = £6.79 B. Incorrect as calculated the exponent of * is mistakenly used without a negative sign. p0 –c0=[X-F0(T)](1+r)+T p0 –c0=[X-F0(T)](1+r)-T =c0