Special Exotic Option Pricing Approach [closed]

Question

I am currently stuck with the following problem:

You need to price the following exotic option, where the share price of Stock ABC is the underlying:

• Time to maturity: 2 years

• Right to exercise: Only at maturity

• Payoffs: You receive or pay the minimum of (𝑆𝑇 − 𝑏) and (𝑎 − 𝑆𝑇), where 𝑆𝑇 is the stock price at maturity 𝑇. 𝑎 and 𝑏 are positive constants, set to 𝑎 = 𝐸𝑈𝑅 80 and 𝑏 = 𝐸𝑈𝑅 35 in our contract.

QUESTION:

Derive a pricing formula for the exotic option described above (using BS)

I am not sure what type of exotic option I am encountering, may someone of you can give me a clue?

Answer 1

For homework, I think that people in these forums like when the author explains his current progress/ideas/intuitions.

Try to follow the following steps:

1. Create a plot with axes: $x=S_T, y=\text{payoff}$.
2. Draw the individual payoffs.
3. Use the previous lines in order to determine the global payoff of your product.
4. Usually, the idea behind these exercises is to train you to identify a portfolio of options and/or underlying asset which could replicate these payoffs. In this case, since the payoff can only be determined at maturity, can you find a portfolio of European Call/Put options which could replicate the total payoff of your product ? Hint 1: The key here is to use the slopes of the payoff, and the prices $S_T$ where they change. Hint 2: Remember that you can "invert" a payoff simply by shorting (selling) an option.
5. To avoid arbitrage opportunities, if you can find a portfolio which can replicate the payoff of your financial product for all possible prices $S_T$ at maturity, then the price of your product now has to be the same as the price of the replicating portfolio now.

Just as a final remark, your question lets me think that your product is an option, but I cannot see any optionality in your payoff. Maybe the product is only exercised when the available payoff is greater than 0 ? I do not know, it depends on your problem, but such an optionality would have to be taken into account in steps 3 and 4.

AFTER you have finished these steps, I suggest you have a look at this page.