Role: Head of equity options at Investment Bank Q Situation: Your client (a hedge fund) want to buy a security that allow them to: 1.receive nothing when infinity share price 2.receive $10,000,000...

Role: Head of equity options at Investment Bank Q

Situation:

Your client (a hedge fund) want to buy a security that allow them to:

1.receive nothing when infinity share price

2.receive $10,000,000 from you when infinity share price >= $50 at that time, after which the security expires

The (security) contract is perpetual until it expires and is worthless if Bank Q goes bankrupt.

Assume Investment Bank Q’ shares will trade forever, and the bank never go bankrupt.

The market price of Investment Bank Q’ share today is $40 per share. No dividends or repurchase of shares. Risk-free rate is 0.

At what price do you quote the above security? How do you hedge this security so that Bank Q has no risk?