maturity is 6-months. What is the value of N(d₂ )--the probability of the option being exercised? Formula: d₁= [In S/X + rc T + (o²T)/2] / (0 √T) d₂ = d₁ - 0 √T [Caution: answer the value of N(d₂) using Normsdist in Excel, and not just th
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- Suppose the current stock price of JuJube Inc is ¥100, the risk-free interest rate is 5%, the standard deviation is 25%, the time to maturity is 4 months, the strike price is ¥85, and the price of a call option is ¥25.20. Using the put-call parity relationship, the put option price is closest to A. ¥25.20 B. ¥16.40 C. ¥5.20 D. ¥8.80 E. None of the aboveWhat is the value of d, of a European call option on a non-dividend-paying stock when the stock price is $60, the strike price is $59, the risk-free interest rate is 5% per annum the volatility (Standard Deviation) is 30% per annum, and the time to maturity is three months? c=SN(d,)-Ke-N(₂) where and O√T OA02704 OB0.2167 *√T OC.0.3561 OD.0.1204Suppose a stock is currently trading for $35, and in one period it will either increase to $38 or decrease to $33. If the one-period risk-free rate is 6%, what is the price of a European put option that expires in one period and has an exercise price of $35? $0.51 $2.32 $1.55 $3.00 $0.76
- In this problem we assume the stock price S(t) follows Geometric Brownian Motion described by the following stochastic differential equation: dS = µSdt + o Sdw, where dw is the standard Wiener process and u = 0.13 and o = current stock price is $100 and the stock pays no dividends. 0.20 are constants. The Consider an at-the-money European call option on this stock with 1 year to expiration. What is the most likely value of the option at expiration? Please round your numerical answer to 2 decimal places.Problem 1 Suggest two different portfolios that produce the payoff diagram as in the graph below. Both portfolios may contain any amount of risk-free borrowing or lending, and the underlying stock. Portfolio 1 may contain call options but no put options. Portfolio 2 may contain put options but no call options. Assume the risk-free rate is rf = 10%. 25 20 15 10 5 10 15 20 25 30 35 40 -5 -10 -15 Problem 2 Suppose that a stock is currently trading at $60 per share, and the stock price can only take two possible values one year from now: it can either go up by 25% or down by 20%. The annual risk-free rate is 4%. Assume that the stock pays no dividends. You are interested in pricing an European put option on this stock. The option has a strike price of $66, and its maturity date is exactly one year from now. a) What is the payoff on the put option if the stock price goes up by 25%? b) What is the payoff on the put option if the stock price goes down by 20%? c) What is the price of the put…Assume the price of an non-dividend stock is $40, the annual volatility of the stock is 20%, and the continuous compound risk-free interest rate is 5%. What's the price of a European put option on this stock with delivery price of $40 with 1-year expiration? (The standard normal distribution table is in the attachment or you can use excel function NORMSDIST, and please keep the results with 3 decimal places.) (BS Model-Option Pricing)
- 3. Consider a non-dividend paying stock whose initial stock price is 62 and has a log- volatility of σ = 0.20. The interest rate r = 10%, compounded monthly. Consider a 5-month option with a strike price of 60 in which after exactly 3 months the purchaser may declare this option a (European) call or put option. Assume u = 1.05943 and d = = 0.94390 (a) Compute the values of the binomial lattice for 5 1 month period. 0 1 2 3 4 5 62 (b) Compute the appropriate risk-free rate. (c) Find the risk-neutral probability p of going up? (d) Find the values of call option and put option along this lattice: 0 5.85 1 2 3 4 5 call option 0 1 2 3 4 5 1.40 put optionConsider 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.When the non-dividend paying stock price is $20, the strike price is $20, the risk-free rate is 5%, the volatility is 20% and the time to maturity is 3 months which of the following is the price of a European put option on the stock? N(.) denotes standard normal distribution values. O 20N(-0.1)-20N(-0.2) 20N(-0.2)-20N(-0.1) O 19.7N(-0.2)-20N(-0.1) O None of these O 19.7N(-0.1)-20N (-0.2)
- The market premium, E(RM)−rfis estimated to be 8% per annum, while the risk-free return (rf) is 2.5%. What is the expected return of stock KO if it's beta estimate is βKO=0.55 ? Enter rate in decimal form, rounded to the fourth digit, as in "0.1234"b) Suppose you are given the following information: Current market price of a share= R200 000 Option’s exercise price = R300 000 Time until the option expires= 5 yrs Risk free rate =4% Standard deviation of the returns on the share= 0.35 Required: i. Calculate d1 and d2 ii. Suppose N(d1) =0.7517 and N(d2) =0.4602; calculate the price of the call option on the shareD3) Finance What is the probability that the put option is OTM at maturity if: the Stock is S = $195.00, no dividend is paid, the risk-free rate is r = 2.40%, the strike price is K = 209.00, the maturity is T = 23 months and the parameters are d1 = 0.2328 and d2 = -0.3175?