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Question 4

[5 + 5 + 5 = 15 marks]

Satoshi Nakamoto, the mysterious inventor of Bitcoin and developer of the world’s first

blockchain,4 has approached your financial institution (confidentially of course) for advice on

hedging his existing crypto portfolio. The portfolio is currently worth USD1.2 billion and also

has an income yield (from yield farming) of around 2.5% per annum with simple

compounding. Satoshi (or Ian as he insists on being called) has seen the value of his portfolio

significantly decline over the last two years, due in large part to the latest ‘crypto winter’.5

While there has been a resurgence in bitcoin’s price in 2023, Satoshi/Ian expects a bear

market for the remainder of the year. As such, he is seeking advice on how best to protect

the value of his existing crypto portfolio over the next 4 months. He also does not want to

miss out on any potential upside if the bear market doesn’t eventuate.

You should also perform the following tasks and answer the following questions:

i. Plot the implied volatility from each option type (put/call) as a function of the strike.

ii. Is the implied volatility of one option class higher than the other? If so, explain why.

iii. Does the implied volatility depend on the moneyness of the option? Is so, explain.

iv. What do your results tell you about the observed market prices and their consistency

with the assumptions underlying the Black-Scholes model?

Explanation & Answer

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