Essentials Of Investments
11th Edition
ISBN: 9781260013924
Author: Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher: Mcgraw-hill Education,
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2. Suppose you have the following information concerning a particular options.
Stock price, S = RM 21
Exercise price, K = RM 20
Interest rate, r = 0.08
Maturity, T = 180 days = 0.5
Standard deviation, = 0.5
a. What is correct of the call options using Black-Scholes model?
b. Compute the put options price using Black-Scholes model.
3Suppose a European put options has a price higher than that dictated by the putcall parity.
a. Outline the appropriate arbitrage strategy and graphically prove that the arbitrage is riskless.
Note: Use the call and put options prices you have computed in the previous question 2 above.
b. Name the options/stock strategy used to proof the put-call parity.
c. What would be the extent of your profit in (a) depend on?
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- Please do on paper if possible!arrow_forwardYou buy a put and a call on a stock that expire at time T. They are European options. Both the put and the call have an exercise price of $50. Plot the cash flows at the time of expiry. This strategy has a name. What is it?arrow_forward3. Consider a one-period binomial model with h = 1, S = 100, r = 0.08, u = 1.5, d = 0.8 and 8 = 0. Calculate the price of an American put option on this stock with strike price K = 100. Does early exercise occur?arrow_forward
- What is the gamma of a European call option with the following parameters? As a reminder, gamma is defined as the first derivative of delta with respect to the stock price, or alternatively as the second derivative of the option price with respect to the stock price. s0 = $40k = $40 r = 10%sigma = 20%T = 0.75 years In order to avoid precision issues with Excel, please use an epsilon of 0.0001. (required precision 0.0001 +/- 0.0002) Greeks Reference Guide: Delta = ∂π/∂S Theta = ∂π/∂t Gamma = (∂2π)/(∂S2) Vega = ∂π/∂σ Rho = ∂π/∂rarrow_forwardTick all those statements on options that are correct (and don't tick those statements that are incorrect). B a. The Black-Scholes formula is based on the assumption that the share price follows a geometric Brownian motion. b. If interest is compounded continuously then the put-call parity formula is P+ S(0) = C + Ker where T is the expiry time. An American put option should never be exercised before the expiry time. d. In general the equation S(T) +(K-S(T)) = (S(T)-K)+ +K is valid. e. The put-call parity formula necessarily requires the assumption that the share price follows a geometric Brownain motion. C.arrow_forwardD3(arrow_forward
- Question Which of the following statement(s) is/are true regarding a single-period binominal model with a time period h? I) If X is the expected payoff of a European option in the real world, then the price of the option can be obtained by discounting X at the risk-free interest rate II) To calculate the risk-neutral probability of an increase in stock price, the risk premium of the stock is needed II) In the risk-neutral world, the expected stock price at time h is the forward price for the stock delivering at time h Possible Answers A 1) only B III) only C I) and II) only D 1) and III) only E None of the statement is truearrow_forwardPlease choose on the options and please explainarrow_forwardD4) Consider a two-step binomial tree. What is the delta of the put option if: the futures price is S = 1682.00, the risk-free rate is r = 2.90%, the strike price is K = 1757.00, the maturity is T = 12 months and the tree parameters are u = 1.1357 and d = 0.8620? (keep 4 decimals in your calculations).arrow_forward
- 5. Explain and give appropriate use of the following option trading strategies along with their Payoff.: a. Spreads b. Straddles c. Strangles d. Covered Call and Protective Put. State Put-Call Parity theorem for European options. European put and call options with a strike price of Rs. 24 and expiry in 6-months are trading at Rs. 5.09 and Rs. 7.78, respectively. The current stock price is Rs. 20.37 with a risk-free interest rate continuously compounding equal to 7.48%. Is there an arbitrage opportunity? How can it be exploited?arrow_forwardLet S = $100, K = $95, \sigma = 30%, r = 8%, T = 1, and \delta = 0. For simplicity, let u = 1.3, d = 0.8 and n = 2 (that is, 2 periods). When constructing the binomial tree for the European call option, what is A (Stock Share Purchased in the replicating portfolio) at the first node (Time 0)? Question 11 options: 0.1789 0.3886 1.0000 0.2550 0.6912arrow_forward3. A bear spread payoff has the form g(ST) = max(K₂- ST, 0) - max(K₁ – ST, 0), where 0 < K₁ < K₂. (a) (b) Sketch the payoff diagram. Use the general formula for the European option pricing function to find the time-zero option price of a bear spread.arrow_forward
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