A put option has an N(-d1) of 0.5329. You wish to construct a strategy that mimicks the payoff of a short straddle that shares the same strike as the put above, as well as an appropriate underlying position. If your strategy contains 141 put options, determine how many shares you need to buy or sell to achieve this goal. If you need to buy shares, please input a positive (whole) number. If you need to sell shares, please input a negative (whole) number.
Question
A put option has an N(-d1) of 0.5329. You wish to construct a strategy that mimicks the payoff of a short straddle that shares the same strike as the put above, as well as an appropriate underlying position. If your strategy contains 141 put options, determine how many shares you need to buy or sell to achieve this goal. If you need to buy shares, please input a positive (whole) number. If you need to sell shares, please input a negative (whole) number.
Solution
To construct a strategy that mimics the payoff of a short straddle, you would need to short both a call and a put option at the same strike price. However, in this case, you only have put options. Therefore, you need to create a synthetic short call option using the put options and the underlying asset.
The formula to create a synthetic short call is: Short Call = Short Put + Long Underlying.
Given that N(-d1) is 0.5329, this is the delta of the put option. The delta of the put option ranges from -1 to 0. Since we are shorting the put, the delta becomes positive, i.e., 1 - 0.5329 = 0.4671.
This means for every put option you short, you need to long 0.4671 shares of the underlying to create a synthetic short call.
If your strategy contains 141 put options, the number of shares you need to buy is 141 * 0.4671 = 65.84 shares.
Since we can't buy a fraction of a share, we round it to the nearest whole number. Therefore, you need to buy 66 shares to achieve this goal.
Similar Questions
Please determine the payoff for the following long position in a knock-in put option, based on the price path summary below: Starting price of underlying (at inception): $106.1 Maximum traded price of underlying: $112.65 Minimum traded price of underlying: $96.78 Terminal price of underlying (at maturity): $103.19 Strike rate, K: $102.77 Barrier, H: $110.24 Premium, p: $4.1 (Assume continuous price observations)
In expectation of increased price volatility, an investor purchased a call option and at the same time bought a put option with common exercise prices. The strategy is known as a:Question 9Select one:a.horizontal spread.b.vertical spread.c.short straddle.d.long straddle.
Select the best option strategy for each of the investor objectives by selecting the matching number. (3 marks) Write call options on stocks owned (Covered call) Write put options on stocks owned (Protective put) Buy put options1. Protect against potential losses on stocks owned.2. Generate additional yield on stocks being held for the long term.3. Use a limited amount of money to profit if a stock you believe is going down drops in value.
The investor buys a put option on a security with a strike price of $40 and a premium of $2; and buy a call option on a security with a strike price of $30 and a premium of $4. If price of security at maturity (ST) is $30, his profit will beSelect one:a. $3b. $4c. -$6d. -$4
Please determine the payoff for the following fixed lookback put option, based on the price path summary below: Starting price of underlying (at inception): $25.11 Maximum traded price of underlying: $27.89 Minimum traded price of underlying: $20.75 Terminal price of underlying (at maturity): $26.71 Strike rate, K, (if applicable): $26.16 (Assume continuous price observations)
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.