Exercise IX:

An investor is faced with the choice between buying a plain vanilla put on Hugo Boss stock or investing in a protective put with a maturity of $4$ years.

The following market data are known:

Current price of the Hugo Boss share: $57$

Base price put: $40$

Risk$-$free interest rate: $0\mathrm{.}3\%$

Volatility of the Hugo Boss share: $15\%.$

Evaluate the put option according to the BSM model $(1$ point$)$

At what price can the investor conclude the Protective Put trading strategy?

Name two advantages and disadvantages each of the Protective Put over the Plain Vanilla Put?

At what market expectation does it make sense to invest in a Protective Put?

At what market expectation does it make sense to sell a plain vanilla put?

Exercise X:

An investor buys $100$ Daimler shares at a price of $45$ and sells calls with a strike of $40$ and a premium of $15.$

What is the maximum loss of the investor?

If the call is exercised at a share price of $50,$ what is the investor's expected profit$/$loss$?$