Derivatives Analysis: CAC 40 Futures, Options, and Structured Products

This assignment delves into the analysis of CAC 40 futures and options, covering various aspects of derivatives trading and financial product design. The student is tasked with interpreting market expectations by analyzing April and May futures contracts, calculating and comparing implied dividend yields from settlement prices, and constructing and evaluating options strategies such as strangles and spreads. Furthermore, the assignment explores the pricing of European puts in a simplified financial market and examines the construction of a capital-guaranteed structured product, including the use of a bull spread. The solutions involve quantitative analysis, strategic decision-making, and an understanding of financial market dynamics, providing a comprehensive overview of derivatives and structured products.

Data From the Futures and Options Markets on the CAC 40 are given below :

The spot CAC40 is different due to different time the screenshots have been taken. Please use
for each derivative the corresponding spot from the screenshot.

Exercise 1:
1) Assume I buy today the April and sell the May Futures contract. What are my
expectations as to the CAC 40 ? These are the only positions in my portfolio
Answer
If I buy today futures of CAC 40 for the month of April and short the same futures for the
month of May, I expect short term upward movement in the stock which shall be correctified
in the near term. The second reason for such style of investment is to reduce outflow initially
whereby the long position shall result in outflow and short position shall result in inflow in
order to reduce the total outflow. Further, since the future value of April contract shall rise
faster than the contract value of May, I am considering to make gain out of the same. Thus,
this are the two rational for the proposed style of investment.
2) From the settlement prices of December 2020 and December 2021, extract the implied
dividend yield. Compare and discuss. If needed use an interest rate of 0.2% yearly.
The settlement prices of December 2020 is 4120.5 while the settlement price of December
2021is 3941.
Answer
To infer the implied dividend yield the formula used to price forward contracts has to be
manipulated as follows:
q=−¿
q – dividend (per month)
F0 – Future Price
S0 – Underlying Price (CAC40)
T – Time (months)
r – LIBOR (monthly)
Using the December, 2020 and December 2021 future prices the following implied dividend
yields are calculated. TSettlement prices are estimates of the market-maker based on the last
trades of the day while accounting for the trend of the underlying.
2. Settlement

Dec, 2020 Dec,2021
F0 4120.5 3941
S0 4238,79 CAC40
r 0.0002
q 0,2945% 0,3269%
The dividend yield has increased in the second case as compared to first on difference in S0
and F0 being large.
Exercise 2:
1) With the Call and the Put 4250, build a strangle using the book prices.
The call at the strike price of 4300 and put price at the strike price of 4250 are : 125 (ask
price) and 165.7 (ask price) respectively resulting in total outflow of 290.7 initially. Thus,
there shall be movement of stocks sufficient enough to cover the cost. Thus, lets assume that
at the end the april the price stands at 4600. Thus, the put option shall end valueless while call
option shall have value of roughly 300. Thus, there shall be a margin of 9.3.
2) Redo 1) but using a different strike for the two options.
The call at the strike price of 4375 and put price at the strike price of 4125 are : 90.1 (ask
price) and 118 (ask price) respectively resulting in total outflow of 208.1 initially. Thus, there
shall be movement of stocks sufficient enough to cover the cost. Thus, lets assume that at the
end the april the price stands at 4600. Thus, the put option shall end valueless while call
option shall have value of roughly 225. Thus, there shall be a margin of 16.9.
Exercise 3:
Assume the following financial market:
Today Mid Apr. End Apri.
Stock 17
Bank Acc. 1

Stock 13
Bank Acc. 1
Stock 10 Stock 10
Bank Acc. 1 Bank Acc. 1
Stock 7
Bank Acc. 1
Stock 5
Bank Acc. 1
1) What should be the fair price of a European Put on the stock with strike 11 and
maturing end of April ?
Answer
Today Mid Apr End Apr Due date payment for the put-11
Mid April
UP Today
17A+B=0
Stock
17 0
13A+B=0
Stock
13 A=0 7A+B=8
B=-0 A=-4/3
Cost=0 B=17.33
Stock
10
Stock
10 1 10A+B=1
Cost=-
4/3*10+17.33=4
A=1
Stock 7 B=-9
Stock 5 6 5A+B=6
A=1
B=1
2) Show that your strategy is self-financing (rebalancing costs 0).

Today Mid Apr End Apr Due date payment for the call-11
Rebalancin
g
Stock
17 0
A=0 -2.33
B=0 2.33
A=-4/3
Stock
10 1
B=17.33
A=1 8.67
B=1 -8.67
Stock 5 6
3) Repeat 1 and 2 assuming the Put is American.
Today Mid Apr End Apr Due date payment for the put-11 Mid April Payment Today
Stock 17 0
Stock 13 0
Stock 10 Stock 10 1 1
Stock 7 4
Stock 5 6
Today Mid Apr End Apr Due date payment for the put-11 Rebalancing

Stock
17 0
Stock
13 0
0
Stock
10
Stock
10 1
Stock 7 4
-4
Stock 5 6

Exercise 4:
Here is data for long term options:
Assume you collected 1 billion of euros for a capital guaranteed product on the CAC 40.
Please design one such product at the March 2021 horizon.
If needed, assume interest rate is 1%.
1) Which structured product can you built for a one year maturity?
Answer
Invest 1 Billion/1.01= .9901 Billion Euros
Invest balance in call option: .01 Billion Euros at 4250 strike price
2) Please show how your product changes when you use a bull spread instead of one
option.

Invest 1 Billion/1.01= .9901 Billion Euros
Invest balance in Bull and Spread Strategy whereby Buy the call of 4250 Strike price
and sell the call of 4300 to the tune that net amount invested shall be .01 Billion.