Describe a potential arbitrage strategy if a put price is the same as the negative of a forward if the strike are the same. You need to specify the number of units you would long/short for each instrument, initial cash flow, and final cash flow. An arbitrage oppotunity arises only when the both cash flows are non-negative, and one of them is positive in at least one possible scenario.
To describe a potential arbitrage strategy when a put price is the same as the negative of a forward with the same strike, you would need to execute the following steps:
1. Identify the opportunities: Look for a put option and a forward contract with the same strike price (the price at which the underlying asset can be bought or sold).
2. Calculate the initial cash flow: If the put price and the negative of the forward have the same value, then you can initiate an arbitrage position with zero initial cash flow.
3. Determine the number of units to long/short: To create an arbitrage opportunity, you would typically short (sell) the put option and long (buy) the forward contract. The number of units you would long/short depends on the specific contract specifications and the case at hand. However, to keep things simple, let's assume one unit for each instrument.
4. Monitor the scenario: Arbitrage opportunities arise when both cash flows are non-negative, and at least one of them is positive in at least one possible scenario. So, you want to observe possible outcomes of the underlying asset price movement.
5. Calculate the final cash flow: Based on the potential scenarios, calculate the final cash flow. To ensure an arbitrage opportunity, the final cash flow should always be non-negative.
Let's consider an example to illustrate this strategy:
Example:
Suppose a put option with a strike price of $100 has a price of $10, and a forward contract on the same underlying asset with the same strike price has a value of -$10 (negative value).
- Initial cash flow: $0 (since put price = negative forward value)
- Number of units: One unit each for put option and forward contract
Possible Scenarios:
1. Scenario A: If the underlying asset price falls below $100
- Put option: Exercise the put option and sell the underlying asset at $100. Receive a cash flow of $100.
- Forward contract: Do nothing since the forward contract has a negative value. No cash flow.
Final cash flow: $100 (positive)
2. Scenario B: If the underlying asset price remains at $100 (unchanged)
- Put option: Do not exercise the put option. No cash flow.
- Forward contract: Do nothing since the forward contract has a negative value. No cash flow.
Final cash flow: $0 (non-negative)
3. Scenario C: If the underlying asset price increases above $100
- Put option: Do not exercise the put option. No cash flow.
- Forward contract: Settle the forward contract by selling the underlying asset at the higher market price. Receive a cash flow equivalent to the positive difference between the forward price and the market price.
Final cash flow: Positive if the difference between the forward price and market price is greater than $0. Otherwise, $0 (non-negative).
In this example, the arbitrage opportunity arises in Scenario A, where the final cash flow is positive ($100), meaning you can make a riskless profit. However, in Scenarios B and C, the final cash flow is non-negative but not positive, so no arbitrage opportunity exists.
Keep in mind that actual arbitrage opportunities may involve more complex variables, fees, spreads, or trading constraints. This explanation provides a basic understanding of a potential arbitrage strategy based on the given conditions.