### Case Study

Finance代写 | Risk Management 代写 – 这是金融商科等代写方向

```
Spring 202 2
Dr. Maximilian Schreiter / Franziska Stimper
```

### Financial Instruments & Asset Pricing

### Case Study Tasks

#### General Instructions

Each group has to solve three tasks. The first one shall be solved with a binomial tree model, the second one based upon the Black Scholes Merton framework, and the last one with the help of a simulation. We DO NOT NEED a fancy PRESENTATION. We know that you are capable of building one. We would like to have a **written report** in PowerPoint or Word explaining your calculation steps, solutions, and reasonings. For some tasks, IT might make sense to add a little illustration/chart to bring your point across. Moreover, we would like to have the **underlying models of your calculations** in Excel and/or R.

The aforementioned files need to be submitted to Maximilian Schreiter **by 31 July, midnight (CEST), via email ([email protected]).**

#### Task 1: Risk Management with flexible Call/Put Options

In Risk Management, it is sometimes important to be hedged against movements of prices in both directions, up and down. A great example are volatile input prices where you cannot transfer the fluctuations into selling prices. The hedging tool we want to look at, is an option contract that allows to choose whether the option is a call or a put option during the time to maturity. This way, the buyer of the option contract keeps the flexibility to react on market changes significantly longer while already logging in the possibility to hedge. There are many different potential features, and we are concerned with the following ones:

```
The option has a time to maturity of two years.
At certain points in time during the first year, the holder of the option can choose whether the
option is a European call or a European put.
The points in time, where the option to choose can be executed, are exactly after each quarter
of the first year, i.e., after exactly 3 months, 6 months, 9 months and 12 months.
Once the choice has been made, it cannot be reversed. From that moment onwards the option is
either an ordinary European call or European put option.
The strike price for both, the European call and the European put option, is X=320.
```

Moreover, we know the following about the input price we are concerned with, i.e., the underlying:

```
Current price: 31 0
Volatility of changes in price: 25%
Risk-free rate: 1%
Storage yield: 1% (Just subtract the storage yield from the risk-free rate to arrive at your risk-
neutral drift.)
```

```
Spring 202 2
Dr. Maximilian Schreiter / Franziska Stimper
```

**QUESTIONS**

```
1) Model the input price development with the help of a binomial tree. (4)
2) Describe the payoff function of this financial instrument at maturity and prior to maturity. (7)
3) Price the flexible call/put option as of today. (6)
4) Show the sensitivities of this financial instrument. How is the price of the option changing, if:
o Time to maturity changes (3)
o The volatility of changes in the price changes (3)
o The risk-free rate changes (3)
o Advanced: The number of dates and the dates change (4)
```

#### Task 2: Simple Exotic Option

You need to price the following exotic option, where the share price of **Intel Corp (INTC)** is the underlying:

```
Time to maturity: 1 year
Right to exercise: Only at maturity
Payoffs: You receive the maximum of () and (), where is the stock price at
maturity . and are positive constants, set to = 65 and = 40 in our contract.
```

**QUESTIONS**

```
1) Analyze the ten years monthly stock data of INTC until 31 December 2021 and check how valid
the assumptions of the Black-Scholes-Merton model regarding the stochastic behavior of the
stock are. (Please continue in the Black-Scholes-Merton framework in any case, i.e.,
independent of your results for this task.) (5)
2) Analyze the ten years monthly stock data of INTC and estimate the stocks volatility. (3)
3) Derive a pricing formula for the exotic option described above. (14)
4) Implement the formula in Excel and calculate the option price for the parameters provided
above and with the last stock price of INTC from the data representing the current stock price.
(4)
5) Analyze the dynamics of the option price with respect to changes of and (e.g., in a so called
football field with values along the first column and along the first row. (4)
```

#### Task 3 : Earnout Clause

Consider the following agreement: BuyCo acquires TargetCo. The management of TargetCo has also been a shareholder in the company and they are going to stay on the board of TargetCo for the next three years. This is necessary since much of the customer contacts are tied to them and currently developed innovations rest upon their expertise. To ensure that these managers are well-incentivized although not longer being shareholders they get an earnout clause. An earnout clause is a future contingent payment which is conditioned on a pre-determined (success) event. In our agreement, the earnout clause is structured as follows:

```
Spring 202 2
Dr. Maximilian Schreiter / Franziska Stimper
```

```
Time to maturity of the earnout: 3 years
Payoff: The average of the 12 realized, quarterly earnings before interests and taxes (EBIT) up to
the end of the earnout is compared to a strike of EUR 1 5 million. If the realized average of EBITs
exceeds the strike, managers receive a multiple = 6 of the excess amount. If the realized
average of EBITs ends up below the strike, managers get no payoff. Furthermore, if any of the 12
quarterly EBITs fall below the constant quarterly interest payments, the earnout contract will
cease to exist and no payoff will happen.
```

The following is known about the company and the behavior of its quarterly EBITs:

```
Quarterly EBITs seem to follow a geometric Brownian motion, where the risk neutral
development can be described by:
= 0 (
```

```
1
2 ^2 )+
```

```
With 0 = 13 being the current quarterly EBIT (which is not part of the
average in the earnout contract), = 1 .5%^1 representing the risk-neutral drift rate of the
EBIT, =20% reflecting the volatility of changes in EBIT and ~( 0 , 1 ) being a random
number following a standard normal distribution.
The risk-free interest rate =2% is constant over time.
The company pays interests of = 7 each quarter.
```

**QUESTIONS**

```
1) Model the companys EBIT development with the help of a simulation and present histograms
for the quarterly EBIT at t=1 year (after 4 quarters), t=2 years (after 8 quarters) and T=3 years
(after 12 quarters), respectively. (6)
2) Describe the payoff function of this earnout in mathematical terms or in a function you can
implement via simulation. (4)
3) Model the earnouts payoff on each simulation path and present a histogram of the payoffs in
T=3 years. (4)
4) Estimate todays value of the earnout clause based on your payoff modelling. (2)
5) Estimate the risk-neutral probability to end up in the money, i.e., having a payoff greater than
zero? (2)
6) Assume the real-world drift rate of the EBIT process is equal to 6%. What is the real-world
probability to end up in the money, i.e., having a payoff greater than zero? (4)
7) Please explain why and deviate from each other, and which one you would take to report
the likelihood of a payment to the managers. (3)
8) Advanced 1 : Estimate the risk-adjusted discount rate, i.e., the expected return of the
managers, of this earnout clause. (3)
9) Advanced 2: Why might it make sense to structure an earnout like that in comparison to a
European-style earnout where payoff is just determined based on the EBIT at maturity? (2)
```

(^1) It is like from all the processes of our lecture examples. We just have to make a slight distinction because so far we were considering values while the EBIT is a profit. The discounting of payoffs is still happening based on .