What is the delta hedge (number of options) for call options with a strike of $71.85 required to hedge a single shared that is presently worth $52.9/share and can attain $86.73/share with 40% likelihood or $46.91/share with 60% likelihood? [If your answer is a fraction, please convert it to a decimal for submission]
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- 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 0.265Use 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 0.26Reconsider the determination of the hedge ratio in the two-state model, where we showed that one-third share of stock would hedge one option. What would be the hedge ratio for the following exercise prices: (a) 120, (b) 110, (c) 100, (d) 90? (e) What do you conclude about the hedge ratio as the option becomes progressively more in the money?
- A three-step binomial tree with terminal stock prices being 1.103, 0.875, 0.695, and 0.552. At time 0, if you have the insider information that at the maturity the stock price will be 0.875. Then, will the option premium at time 0 still be same as if you don't have this information, please choose from the answers below? a) Option premium is irrelevant to the private information (about the underlying) that option holder possesses. b) As in that case, the risk neutral probability of the impossible sample paths become zero.parts c, d, e Suppose an investor is considering a multi option strategy on a stock with a currentprice of $100. The following strategy is called a strangle. The investor purchases a call optionwith a strike price of $110 for a premium of $5 and purchases a put option with a strike priceof $90 for a premium of $3.a) Draw a payout diagram for the strangle option strategy at expiration.b) Determine the breakeven points for the strangle option strategy.c) Suppose the stock price at expiration is $120. What is the profit for the strangle optionstrategy?d) Suppose the stock price at expiration is $85. What is the profit for the strangle optionstrategy?e) What is the investor speculating on with her option strategy?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
- Data: S0 = 120; X = 126; 1+r = 1.05. The two possibilities for ST are 150 and 102. (Round to 2 decimal places). The range of S is 48 while that of C is 24 across the two states. What is the hedge ratio of the call? Hedge ratio ? Calculate the value of a call option on the stock with an exercise price of 126. (Do not use continuous compounding to calculate the present value of X in this example because we are using a two-state model here; the assumed 5% interest rate is an effective rate per period.) Call value ?Finance (a) Consider a portfolio with a Delta of 100, a Gamma of -20, and a Vega of -10. There are two traded options available: Traded options 1 Traded options 2 Delta 0.2 -0.1 Gamma Vega 0.01 0.05 0.5 0.3 What position in the traded option and/or underlying stock would make the portfolio Gamma and Vega neutral? (Required: Show your work step by step)QUESTION 2. Consider a stock valued So at time t = 0, and taking only two possible values S1 = S, or Si = S1 at time t = 1, with S, < I1. a) Compute the initial portfolio allocation (a, 3) of a portfolio made of a units of stock and $B in cash, hedging the call option with strike price K e [S,,3¡] and claim payoff Si – K if Si = 3ı C = (Si – K)* $0 if S = S1, at time t = 1. b) Show that the risky asset allocation a satisfies the condition a € [0, 1]. c) Compute the Superhedging Risk Measure SRMc' of the claim C = (S1 – K)+.
- Reconsider the determination of the hedge ratio in the two-state model where we showed that one-third share of stock would hedge one option. The possible end-of-year stock prices, uS0 = $135 (up state) and dS0 = $100 (down state). What would be the call option hedge ratio for each of the following exercise prices: $135, $122, $111, $100, given the possible end-of-year stock prices, uS0 = $135 (up state) and dS0 = $100 (down state)? Exercise Price Hedge Ratio $135 ? $122 ? $111 ? $100 ?Reconsider the determination of the hedge ratio in the two-state model where we showed that one-third share of stock would hedge one option. The possible end-of-year stock prices, uS0 = $135 (up state) and dS0 = $115 (down state). Required: What would be the call option hedge ratio for each of the following exercise prices: $135, $127, $120, $115, given the possible end-of-year stock prices, uS0 = $135 (up state) and dS0 = $115 (down state)? What do you conclude about the hedge ratio as the option becomes progressively more in the money?Label the following for this diagram: a. Name of options payoff b. Identify whether positive or negative premium c. Identify breakeven point d. What is the profit or loss when stock price is S60 at maturity e. Suppose you have this options position, should you exercise your right (if any) assuming that the stock price is $60 at maturity? Option Payoffs and Profits Long put $40 $20 $0 Option Payoff Option Profit Exerche Price $20 S40 $20 $40 S60 $80. Stock Price At Maturity Payoff and Profit