4. A speculator has a portfolio which is short in a European call with strike K1 and long in a European call with strike K2 . These two calls have the same maturity and underlying asset, but K1 > K2. Say the asset has value S(T) at maturity. This portfolio is called a bull spread.
(a) Write an equation to describe the payoff at maturity of the bull spread.
(b) For each of the three cases S(T) < K2 < K1 , K2 < S(T) < K1 and K2 < K1 < S(T), what are the payoffs at maturity in terms of K1, K2 and S(T)?
(c) For this bull spread, plot the payoff at maturity against the asset price S(T), labelling all significant points.
(d) A speculator believes that at maturity the underlying price will be more than K2 but less than K1. Assume this speculator’s prediction is correct. Why is it better for the speculator to have the bull spread portfolio described above, rather than just a European call with strike K2 ?
(e) A bear spread is a portfolio consisting of a short put with strike K1 and a long put with strike K2 with the same maturities and underlying asset but K1 < K2 . Say the asset has value S(T) at maturity. Write an equation to describe the payoff at maturity for this bear spread. Then, for each of the three cases S(T) < K1 < K2 , K1 < S(T) < K2 and K1 < K2 < S(T), determine the payoffs at expiry in terms of K1, K2 and S(T). Finally, for this bear spread, plot the payoff at maturity against the asset price S(T), labelling all significant points.
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4. A speculator has a portfolio which is short in a European call with strike K1...
The goal of this project is to examine option trading strategies. The project requires you to work in Excel with the provided spreadsheet. A) Bull Spread Payoff Long call option K1 = Short call option K2 = Stock Price (ST) Total Payoff $0.00 $5.00 $10.00 $15.00 $20.00 $25.00 $30.00 $35.00 $40.00 $45.00 $50.00 $55.00 $60.00 A) Consider buying a call option with a strike of $20 and a selling call option with strike of $30. Fill in the table for...
The table below gives today’s prices of six-month European put and call options written on a share of ABC stock at different strike prices. The stock does not pay a dividend and the risk-free interest rate is 0% per annum. Call Price ($) Strike Price ($) Put Price ($) 13.1 105 8.2 9.7 110 9.7 7.9 115 12.9 Using call options with strike prices of 105 and 110, create a bear spread and show in a table the profit of the...
4. A trader buys a European call option and sells a European put option. The options have the same underlying asset, strike price and maturity. Show that the trader's position is equivalent to a forward contract with delivery price that is equal to the strike price of the options.
A trader buys a European call option and sells (short) a European put option. The options have the same underlying asset, strike price, and maturity. Describe the trader’s position. The trader monitors the market continuously and finds at one point that the call is significantly overpriced relative to fair value. What strategy is available for the trader to lock in a profit at current prices?
Assume the following premia: Strike $950 Call $120.405 93.809 84.470 71.802 51.873 Put $51.777 74.201 1000 1020 84.470 101.214 1050 1107 137.167 I 1) Suppose you invest in the S&P stock index for $1000, buy a 950-strike put, and sell a 1050- strike call. Draw a profit diagram for this position. What is the net option premium? 2) Here is a quote from an investment website about an investment strategy using options: One strategy investors apply is a "synthetic stock."...
the cash price of a one year treasury bill is 95 per 100 of face value. a 2 year bond with a face value of 100usd that pays annual coupons of 8. The table below gives today's prices of six-month European put and call options written on a share of ABC stock at different strike prices. The stock does not pay a dividend and the risk-free interest rate is 0% per annum. Put Price (S) Call Price (S) 13.1 9.7...
Exercise 1. An investor has a short position in a European put on a share for $4. The stock price is $40 and the strike price is $41 Under what cicum be cuercise (b) Under what circumstance does the investor make a profit? (c) Draw a payoff diagram plotting the investor's payoff as a function of Sr. (d) Draw a profit diagram plotting the investor's profit as a function of ST. (e) Suppose now the investor enters also into a...
6. The following table shows the premiums of European call and put options having the same underlying stock, the same time to expiration but different strike prices: StrikeCall Premium Put Premium $20 $23 $25 $3.59 $2.45 $1.89 $2.64 $4.36 $5.70 You use the above call and put options to construct an asymmetric butterfly spread with the following characteristics (i) The maximum payoff of 6 is attained when the stock price at expiration is 23 (ii) The payoff is strictly positive...
The price of a European call that expires in six months and has a strike price of $49 is $4.5. The underlying stock price is $50, and a dividend of $1.00 is expected in three months. The term structure is flat, with all risk-free interest rates being 10%. a. What is the price of a European put option that expires in six months and has a strike price of $49? [1 mark] b. Explain in detail the arbitrage opportunities if...
3. (10 pts) For each k e [0, 1,2,..., 301 the symbol S(k) denotes the price of the stock at time k. A European call option with strike 90 and expiration n- 30 costs 15. A European put option with strike 100 and expiration 30 costs 11. Both options have the same stock as their underlying security. What is the price of the security whose payoff structure is 7S (30) 630, if S(30) 100, S(30)-30, if 90 S(30) S 100,...