A synthetic forward contract is a way of creating a position that is equivalent to a regular forward contract, which is an agreement to buy or sell an asset at a fixed price and date in the future. A synthetic forward contract uses two options, a call and a put, with the same strike price and expiration date, to simulate the forward contract.
A call option gives the buyer the right, but not the obligation, to buy the underlying asset at the strike price before or on the expiration date. A put option gives the buyer the right, but not the obligation, to sell the underlying asset at the strike price before or on the expiration date.
To create a synthetic forward contract, an investor can buy a call option and sell a put option with the same strike price and expiration date. This means that the investor has the right to buy the asset and the obligation to sell the asset at the same price and date. This is equivalent to agreeing to buy the asset at that price and date in advance, which is what a forward contract does.
Alternatively, an investor can sell a call option and buy a put option with the same strike price and expiration date. This means that the investor has the obligation to sell the asset and the right to buy the asset at the same price and date. This is equivalent to agreeing to sell the asset at that price and date in advance, which is what a forward contract does.
The advantage of a synthetic forward contract is that it does not require a counterparty, which reduces the risk of default or non-performance. However, the disadvantage is that it requires paying a net option premium, which is the difference between the price of the call option and the put option. This premium represents the cost of creating the synthetic forward contract.
Basic Theory:
A synthetic forward is created by combining a spot position in an asset with a position in options. This combination replicates the payoffs and risks of a traditional forward contract but offers greater flexibility. The two main components of a synthetic forward are:
- Spot Position: Owning or borrowing the underlying asset.
- Options Position: Buying call options and selling put options on the same underlying asset with the same expiration date.
By strategically selecting the strike prices of the options, investors can tailor the synthetic forward to their specific needs, achieving a desired cost or profit profile.
Procedures:
To create a synthetic forward in Excel, follow these steps:
- Gather Data:
- Spot price of the underlying asset
- Risk-free interest rate
- Time to expiration
- Determine Strike Prices: Decide on the call and put strike prices based on your risk tolerance and profit objectives.
- Calculate Option Prices: Use the Black-Scholes option pricing model in Excel to calculate the prices of the call and put options.
- Construct the Synthetic Forward:
- Buy the call option.
- Sell the put option.
- Calculate the net cost or profit of the options position.
- Monitor and Adjust: Periodically reassess market conditions and adjust the synthetic forward as needed.
Comprehensive Explanation:
Let’s consider a scenario where an investor wants exposure to XYZ stock, currently priced at $100, without actually purchasing the stock.
- Gather Data:
- Spot Price (S) = $100
- Risk-free Interest Rate (r) = 5%
- Time to Expiration (T) = 6 months
- Determine Strike Prices:
- Call Option Strike Price (Kc) = $110
- Put Option Strike Price (Kp) = $90
- Calculate Option Prices:
- Call Option Price = BS_CALL(S, Kc, r, T, volatility)
- Put Option Price = BS_PUT(S, Kp, r, T, volatility)
- Construct the Synthetic Forward:
- Buy Call Option: -$10 (Cost of call option)
- Sell Put Option: +$10 (Premium received from put option)
- Net Cost = -$10
- Monitor and Adjust: Reassess market conditions, and adjust strike prices if necessary.
Excel Table:
| A | B | C | |
|---|---|---|---|
| 1 | Inputs | Values | |
| 2 | Spot Price (S) | $100 | |
| 3 | Risk-free Rate (r) | 5% | |
| 4 | Time to Expiration (T) | 6 months | |
| 5 | Call Strike Price (Kc) | $110 | |
| 6 | Put Strike Price (Kp) | $90 | |
| 8 | Calculations | Formulas | Results |
| 9 | Call Option Price | BS_CALL(B2, B5, B3, B4, volatility) | $16.53 |
| 10 | Put Option Price | BS_PUT(B2, B6, B3, B4, volatility) | $13.45 |
| 11 | Net Cost | =B9 – B10 | -$3.08 |
Result:
The net cost of the synthetic forward is -$3.08, indicating the amount paid to create the customized exposure to XYZ stock.
Other Approaches:
- Adjusting Strike Prices: Modify strike prices based on market expectations or risk preferences.
- Using Different Option Strategies: Explore other option combinations, such as collars or ratio spreads, to achieve specific risk-reward profiles.
- Dynamic Hedging: Continuously adjust the options position to maintain the desired exposure as market conditions change.
