A Quanto option is a type of option that allows you to buy or sell an asset in one currency but receive or pay the price in another currency at a fixed exchange rate. For example, if you buy a Quanto call option on a stock that is denominated in euros (EUR) but you live in the U.S., you can exercise the option and sell the stock in euros, but you will receive the payment in U.S. dollars (USD) at the exchange rate that was agreed upon when you bought the option.
The advantage of a Quanto option is that it eliminates the risk of currency fluctuations affecting your returns. You are only exposed to the risk of changes in the price of the underlying asset, not to changes in the exchange rate. This makes Quanto options attractive for investors who want to invest in foreign assets but are concerned about currency risk.
The disadvantage of a Quanto option is that it may have higher costs than a regular option, such as higher premiums and commissions. This is because Quanto options are less liquid and more customized than regular options, and they require more complex calculations and transactions. Also, Quanto options may have lower volatility than regular options, because they have fixed exchange rates and less sensitivity to market movements.
Basic Theory
A Quanto option is named after the Italian word for “as” or “like,” emphasizing its purpose to make one asset behave “as if” it were denominated in another currency. These options are often used to mitigate currency risk in international investments. In a Quanto option, the payoff is in a fixed currency, irrespective of the currency in which the underlying asset is denominated.
Procedures in Excel
To model Quanto options in Excel, we need to consider the following key components:
- Underlying Asset Price (S): The current price of the asset in its native currency.
- Strike Price (K): The price at which the option can be exercised.
- Exchange Rate (FX): The current exchange rate between the asset’s native currency and the fixed currency.
- Quanto Factor (QF): A constant factor used to adjust the payoff to the fixed currency.
Excel Formula for Quanto Option Payoff
Assuming a call option, the Quanto option payoff (P) can be calculated using the following formula:
Where:
represents the time value factor based on the risk-free interest rate (r) and time to expiration (T).- X is an additional premium paid for the Quanto feature.
Example
Let’s consider a scenario with the following values:
- Underlying Asset Price (S): $100
- Strike Price (K): $95
- Exchange Rate (FX): 1.2 (1 unit of native currency equals 1.2 units of fixed currency)
- Quanto Factor (QF): 0.9
- Risk-free Interest Rate (r): 3%
- Time to Expiration (T): 1 year
- Additional Quanto Premium (X): $2
Excel Calculation
- Calculate :
- Calculate the Quanto Option Payoff (P):
Excel Table
| Parameter | Value |
|---|---|
| Underlying Asset Price | $100 |
| Strike Price | $95 |
| Exchange Rate | 1.2 |
| Quanto Factor | 0.9 |
| Risk-free Interest Rate | 3% |
| Time to Expiration | 1 year |
| Additional Premium (X) | $2 |
Other Approaches
- Monte Carlo Simulation: Simulating various scenarios can provide a more comprehensive understanding of potential outcomes.
- VBA (Visual Basic for Applications): For complex calculations or iterative processes, VBA can enhance the functionality and automate tasks within Excel.
- Sensitivity Analysis: Assess how changes in parameters (e.g., exchange rate, volatility) impact the Quanto option’s value.
