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A client has requested the bank to provide a customized call option on a listed equity.

A client has requested the bank to provide a customized call option on a listed equity. The client wants to have a European style option to acquire 100,000 shares of XYZ Corporation with a strike price of $100 and an exercise date one year from now. The shares of XYZ Corporation are currently trading in the market at $90 and the bank does not currently own any shares. Firstly, explain the factors that the bank would need to take into account in order to determine the pricing of this option for the client. Secondly, if the implied volatility for XYZ Corporation for the coming year has been estimated at 25% what would be the fair value price for this call. Thirdly, provide an illustration of the different outcomes and risk scenarios for the client. Fourthly, discuss how the bank should implement dynamic delta hedging as a suitable risk management strategy for its exposure.

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