You have written (sold) a three-month European call option at a strike price of $500. The current stock price (So) is $492.00, the annual risk-free interest rate is 4%, and the volatility of the underlying is 10%. Construct a delta hedge of this position using the underlying asset. Report your answer in the number of shares of the underlying purchased/sold. (Positive values indicate a purchase, negative a short)

Give typing answer with explanation and conclusion You are considering purchasing a put on a stock with a current price of $33. The exercise price is $35, and the price of the corresponding call option is $3.25. According to the put-call parity theorem, if the risk-free rate of interest is 4% and there are 90 days until expiration, the value of the put should be:

A collar is established by buying a share of stock for $54, buying a 6-month put option with exercise price $47, and writing a 6-month call option with exercise price $61. On the basis of the volatility of the stock, you calculate that for a strike price of $47 and expiration of 6 months, N(d1) = 0.7298, whereas for the exercise price of $61, N(d1) = 0.6374. Required: What will be the gain or loss on the collar if the stock price increases by $1? What happens to the delta of the portfolio if the stock price becomes very large? What happens to the delta of the portfolio if the stock price becomes very small?

In a financial market a stock is traded with a current price of 50. Next period the priceof the stock can either go up with 30 per cent or go down with 25 per cent. Risk-freedebt is available with an interest rate of 8 per cent. Also traded are European optionson the stock with an exercise price of 45 and a time to maturity of 1, i.e. they maturenext period.i) Find prices of Arrow-Debreu securities.ii) Calculate the price of a call option by constructing and pricing areplicating portfolio.

1. For each of the following cases, calculate (i) the cashflow paid or received today on entering the position, (ii) the gross payoff at expiry, and (iii) the net payoff from your option trading All options are European style and cover 100 shares in the underlying asset. a) You enter a long call option with a strike price of $6 and premium of $2.30. At expiry, the share price is $7.80. b) You enter a long call option with a strike price of $9 and premium of $0.80. At expiry, the share price is $7.90. c) You enter a short call option with an exercise price of $5 and premium of $0.70. The share price at expiry is $5.40. d) You enter a short call option with an exercise price of $5 and premium of $0.70. The share price at expiry is $4.90. e) You buy a long - put option with a strike price of $10 for a premium of $ 1.20. At expiry, the share price is $8.50. f) You write (i. e., short) a put option with strike price $7 for a premium of $0.60. At expiry, the share price is $5.

The one-year futures price on a particular stock-index portfolio is 2,620, the stock index currently is 2,600, the one-year risk-free interest rate is 2.0%, and the year-end dividend that will be paid on a $2,600 investment in the index portfolio is $25. Required: By how much is the contract mispriced? (Input the amount as positive value.) The futures price is its "proper" or parity value.

You buy a share of stock, write a 1-year call option with X = $85, and buy a 1-year put option with X = $85. Your net outlay to establish the entire portfolio is $83.3. Required: What is the payoff of your portfolio? What must be the risk-free interest rate? The stock pays no dividends. Note: Round your answer to 2 decimal places.

D6) You use the Black Scholes model to price a Call option on a stock with discrete dividends. The dividends will be given in months 1, 5, and 9, each 3 USD. The current value of the stock is 105 USD, the strike price is 90 USD, the continuously compounded annual risk-free rate is 0.05, the volatility is 0.08, the time to maturity is 12 months. Calculate the price of the option.

A stock is currently selling for $39. In one period, the stock will move up by a factor of 1.29 or down by a factor of .53. A call option with a strike price of $50 is available. If the risk-free rate of interest is 2.5 percent for this period, what is the value of the call option?