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Answer: An increase in Ethereum’s (ETH) spot price will increase the exchange option’s value
The **false** statement is **C**. For an exchange option, the payoff is essentially: $$\max(S_{BTC} - 14S_{ETH}, 0)$$ So, if the ETH spot price rises, the option becomes **less valuable**, because the cost of exercising the option increases. Why the others are true: - **A**: In the Margrabe exchange option model, the risk-free rate does not affect value when there are no dividend yields/carry effects. - **B**: Higher correlation lowers the volatility of the exchange ratio, so option value falls. - **D**: A higher BTC spot price makes the option more valuable. Therefore, **C** is the incorrect statement.
Author: Manit Arora
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Q-732.1. Consider a one-year exchange option to give up 14.0 units of Ethereum (aka, ether or ETH) for one unit of Bitcoin (BTC). The current price of Bitcoin is $4,200.00 BTC and the current price of one unit of ether is $300.00 ETH. The risk-free interest rate is 2.0% per annum with continuous compounding. The per annum volatility of Bitcoin is 50.0% and the volatility of Ethereum is 38.0%. Their correlation, . We can price an exchange option with a simple variation on the Black-Scholes-Merton called the Margrabe variation. Using the Margrabe under these assumptions, the price of this BTC-for-ETH exchange option is $723.11. Further, each of the following statements, ceteris paribus, is true EXCEPT which is false?
A
A higher risk-free rate has no impact on this exchange option’s value
B
A higher correlation implies a lower exchange option value
C
An increase in Ethereum’s (ETH) spot price will increase the exchange option’s value
D
An increase in the Bitcoin (BTC) spot price implies an increase in the exchange option’s value
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