Essay about Solution for Payoff Diagram Problem Set

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Solution for Payoff Diagram Problem Set
1. Positions
What is the difference between a long forward position and a short forward position?
With a long forward position, you are obligated to buy in the future at a pre-determined price.
With a short forward position, you are obligated to to sell.
2. Forwards and Calls
What is the difference between (a)entering into a long forward contract when the forward price is
$50 and (b) taking a long position in a call option with a strike price of$50?
The payoffs at expiration will be very different.

With the long forward position there is potential for a loss in the future if ST < 50.

With a long call option position there is no downside risk.
3. Investment Strategies
You would like to speculate on the rise in the price of a certain stock. The current stock price is $29 and a 3-month call with a strike of $30 costs $2.90. You have $5,800 to invest. Identify two alter-

native strategies, one involving investment in the stock and the other involving investment in the option. What are the potential gains and losses from each?
Strategy 1 - Invest all of your money in the stock.
⇒ Buy $5,800
$29 = 200 shares of the stock.
Total profit in 3 months:200(S3 − $29) = 200S3 − F V (5800)
Total payoff in 3 months:200S3
Strategy 2 - Invest all of your money in call options.
⇒ Buy $5,800
$2.9 = 2000 call options.
Total profit in 3 months:2000 ∗ max(0, S3 − 30) − F V (5800)
Total payoff in 3 months:2000 ∗ max(0, S3 − 30)
4. Combining Positions
Describe the payoff from the following portfolio: a long forward contract on an asset and a long
European put option on the asset with the same maturity as the forward contract and a strike price that is equal to the forward price of the asset at the time the portfolio is set up.
Long a forward contract:
→ P ayof f = St − X
P ayof f

X

ST

Long a European put:
→ P ayof f = max(0, X − ST )

2

P ayof f
❅
❅
❅
❅
❅
❅

ST

❅
❅

X

Combine the two:
→ P ayof f = max(0, ST − X)
P ayof f

X

ST

5. Combining Positions
”A long forward contract is equivalent to a long position in a European call and a short position in a European put.” Explain this
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