You are given the following information concerning options on a particular stock: Stock price= Exercise price= Risk-free rate= Maturity= Standard deviation= Intrinsic value=$ $83 $80 Time premium of the call option=$ 6% per year, compounded continuously 6 months (a)What is the intrinsic value of the call option? (Please keep two digits after the decimal point.) 47% per year (b)What is the time premium of the call option? (Please keep two digits after the decimal point.)
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- Suppose that a call option with a strike price of $48 expires in one year and has a current market price of $5.17. The market price of the underlying stock is $46.25, and the risk-free rate is 1%. Use put-call parity to calculate the price of a put option on the same underlying stock with a strike of $48 and an expiration of one year. The price of a put option on the same underlying stock with a strike of $48 and an expiration of one year is $. (Round to the nearest cent.)Use the Black-Scholes formula to find the value of a call option based on the following inputs. (Round your final answer to 2 decimal places. Do not round intermediate calculations.) Stock price Exercise price Interest rate Dividend yield Time to expiration Standard deviation of stock's returns Call value GA $ $ $ 48 60 0.07 0.04 0.50 0.26Consider the following information on a particular stock: Stock price = $89 Exercise price = $85 Risk-free rate = 3% per year, compounded continuously Maturity = 8 months Standard deviation = 59% per year 1. What is the delta of a call option? 2. What is the delta of a put option?
- Use the Black-Scholes formula to find the value of a call option based on the following inputs. Note: Do not round intermediate calculations. Round your final answer to 2 decimal places. Stock price Exercise price Interest rate Dividend yield Time to expiration Standard deviation of stock's returns Call value $ 51 $ 64 0.068 0.04 0.50 0.265You are pricing options with the following characteristics: •Current stock price (St): $35.60 •Exercise price (X): $50 •Time to expiration (T-t): 9 months •Risk-free rate (rf): 3.25% •Volatility (0): 45% (a): What is the Black-Scholes value of call option? In your hand-written solution, provide the calculations of d1,d2, and the final call price. Use Excel or another spreadsheet program to compute the values of N(d1) and N(d2). See the notes for details. (b): Using put-call parity, what is the value of a put option? For this case, assume continuous compounding, which implies that PVt(X)=e-r(T-t).X.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 X
- Suppose a stock is currently (time t = 0) worth 100. Further, suppose the one year annually compounded interest rate is 2%, and the two year annually compounded rate is 3%. Find the following:a) The forward price for a forward contract on the stock with maturity year T1 = 1. b) The forward price for a forward contract on the stock with maturity year T2 = 2.c) The forward price for a forward contract with maturity T1 = 1 on a ZCB with maturity T2 = 2.d) The forward price for a forward contract with maturity T1 = 1 on a forward contract on the stock with maturity T2 = 2 and delivery price K = 101.Using the binomial call option model to find the current value of a call option with a $25 exercise price on a stock currently priced at $26. Assume the option expires at the end of two periods, the riskless interest rate is ½ percent per period. What are the hedge ratios?What is the value of a put option if the underlying stock price is $44, the strike price is $37, the underlying stock volatility is 49 percent, and the risk-free rate is 5.6 percent? Assume the option has 137 days to expiration. (Use 365 days in a year. Do not round intermediate calculations. Round your answer to 2 decimal places.) Value of a put option
- What is the value of a call option if the underlying stock price is $82, the strike price is $90, the underlying stock volatility is 51 percent, and the risk-free rate is 3 percent? Assume the option has 62 days to expiration. (Use 365 days in a year. Do not round intermediate calculations. Round your answer to 2 decimal places.) Value of a call optionIn 1973, Fischer Black and Myron Scholes developed the Black-Scholes option pricing model (OPM). (1) What assumptions underlie the OPM? (2) Write out the three equations that constitute the model. (3) According to the OPM, what is the value of a call option with the following characteristics? Stock price = 27.00 Strike price = 25.00 Time to expiration = 6 months = 0.5 years Risk-free rate = 6.0% Stock return standard deviation = 0.49Find the implied volatility (to 2 decimals, for example, �=8.23% ) of a Put option with a time to expiration of 11 months and a price of $6.13 The stock is currently trading at $47. The riskless rate is 2% per annum, and the strike/exercise price of the option is $50. Hint: compute the Put price using the same formula as in exercise 4 , as a function of the volatility �. Then use Solver to change the volatility cell in order to obtain a price of $6.13 \table[[�1=,-0.0614997,,So =,47],[�2=,,4,�=,50],[,,,�=,2%