a
To compute:The Value of a stock-plus-put position as on the ending date of the option.
Introduction:
Put-Call parity relationship: It is a relationship defined among the amounts of European put options and European call options of the given same class. The condition implied here is that the underlying asset, strike price, and expiration dates are the same in both the options. The Put-Call
Parity equation is as follows:
Where C= Call premium
P=Put premium
X=Strike Price of Call and Put
r=Annual interest rate
t= Time in years
S0= Initial price of underlying
b
To compute: The value of the portfolio as on the ending date of the option when portfolio includes a call option and zero-coupon bond with face value (X+D) and make sure its value equals the stock plus-put portfolio.
Introduction:
Value of the portfolio:It is also called as the portfolio value. The
c.
To compute: The cost of establishing above said portfolios and derives the put-call parity relationship.
Introduction:
Put-Call parity relationship: It is a relationship defined among the amounts of European put options and European call options of the given same class. The condition implied here is that the underlying asset, strike price, and expiration dates are the same in both the options. The Put-Call Parity equation is as follows:
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- Consider a European call option on a non-dividend-paying stock where the stock price is $33, the strike price is $36, the risk-free rate is 6% per annum, the volatility is 25% per annum and the time to maturity is 6 months. (a) Calculate u and d for a one-step binomial tree. (b) Value the option using a non arbitrage argument. (c) Assume that the option is a put instead of a call. Value the option using the risk neutral approach. (d) Verify that the European call and European put prices found in (b) and (c) satisfy the put-call parity.arrow_forwardLet C be the price of a call option that enables its holder to buy one share of a stock at an exercise price K at time t; also, let P be the price of a European put option that enables its holder to sale one share or the stock for the amount K at time t. Let S be the price of the stock at time 0. Then, assuming that interest is continuously discounted at a nominal rate r, either S+P-C=Ke-rt or there is an arbitrage opportunity. Question: How do I verify that the strategy of selling one share of stock, selling one put option, and buying one call option always results in a positive win if S+P-C>Ke-rt ?arrow_forwardConsider a European call option and a European put option that have the same underlying stock, the same strike price K = 40, and the same expiration date 6 months from now. The current stock price is $45. a) Suppose the annualized risk-free rate r = 2%, what is the difference between the call premium and the put premium implied by no-arbitrage? b) Suppose the annualized risk-free borrowing rate = 4%, and the annualized risk-free lending rate = 2%. Find the maximum and minimum difference between the call premium and the put premium, i.e., C − P such that there is no arbitrage opportunities.arrow_forward
- Consider two put options on different stocks. The table below reports the relevant information for both options: Put optionTime to maturityCurrent price of underlying stockStrike priceVolatility ( )X1 year$27$1830%Y1 year$25$2030%All else equal, which put option has a lower premium? A.Put option Y B.Put option Xarrow_forwardConsider the 1-period binomial model with a bond with A(0) = 60 and A(1) = 70 and a stock with S(0) = 4X and S^u(1) 6Y and S^d(1) = 3Z. = 1. What is the price (payoff) C(1) of a call option with strike price 28? 2. same... with strike price 45? 3. same... with strike price 72? 4. Set up a system of linear equations to determine a replicating portfolio for the call option from part 2 (strike price 45). 5. Solve it and determine the price C(O). 6. Compute, tabulate, and plot the price C(O) as you vary the strike price of the option from 28, 29, ..., 71, 72.arrow_forwardForward prices of the form Fo = S,e"" are sometimes referred to as “risk-adjusted expected future spot prices". If a stock's expected annualized log return is a (i.e. E[Sr] Soear, or – In ("5") = a), show that the expected annualized log return over the period So t = 0 → T (i.e. the rate of appreciation in F) on a forward contract with maturity T years written on that stock must be equal to the risk premium a – r, where r is the annualized risk-free rate. Explain the surprising result that an asset that requires zero initialarrow_forward
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- You are evaluating a put option based on the following information: P = Ke-H•N(-d,) – S-N(-d,) Stock price, So Exercise price, k = RM 11 = RM 10 = 0.10 Maturity, T= 90 days = 0.25 Standard deviation, o = 0.5 Interest rate, r Calculate the fair value of the put based on Black-Scholes pricing model. Cumulative normal distribution table is provided at the back.arrow_forwardConsider a portfolio consisting of one share and several European call options with the same expiry, but different strike prices. The payoff diagram of the portfolio is given by the following figure. Find the strike prices and the positions of each call option. Portfolio payoff 25 20 15 10 15 20 25 30 Stock price Payoffarrow_forwardPlease explain both a and b Thanksarrow_forward
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