You are bullish on Nvidia $($NVDA$)$ company's stock and want to establish a long

position. However, you only have limited capital available. Construct a synthetic long

position in NVDA stock using European$-$style options, assuming put$-$call parity holds

true. Let's assume the following for NVDA stock:

Current Stock Price: $$200$

Desired Strike Price $($K$)$: $$180$

Expiration Date $($T$)$: July $19$th$,2024$

Call premium: $$15$

Put premium: $$10$

a$.$ What two European$-$style option transactions would you need to execute to create

a synthetic long position in $100$ shares of NVDA stock?

b$.$ Explain how this strategy replicates the price movement of owning the underlying

stock.

c$.$ What is the cost of this synthetic long position?

d$.$ Briefly compare the profit and loss potential of this strategy compared to directly

buying shares of NVDA stock.

e$.$ What is a key limitation of using European$-$style options in this strategy?

f$.$ BONUS: What is the implied risk free rate given the inputs above.