financial modelling

When firms pay dividends, stock prices would decrease by the amounts of dividends on ex-dividend dates
as stocks begin trading without the dividend value. You are motivated to incorporate the discrete nature
of dividends in your option pricing. As per the below dividend schedule, you need to obtain the path on
the scheduled dividend dates and then adjust stock price pro rata to calculate a new option price under
discrete dividends.
= 100 with volatility = 25% where continuously compounded risk free rate is = 0.15%. Suppose
an option with maturity = 0.5 and = 125 time steps (daily evolution during 125 business days)
between = 0 and = . Hence, each time increment is =
0.5
125
. The strike price of the option is 100.
You are required to report call option and put option price, respectively.
Dividend Schedule In the 125 steps Dividend Amount Remarks
In 45 business days 45th out of 125 1.2% of stock price + = − × 0.988
In 105 business days 105th out of 125 1.5% of stock price + = − × 0.985
Complete and fix the FUNCTION named ‘task2’ in the module ‘Q2’. You are required to implement a
section for the treatment of discrete dividends. In general, your task is to find the dividend day (in the
steps) in the binomial tree, shift down the stock price pro rata at that time, and generate remaining path
using the adjusted stock prices.
Task 3
A hedge fund is asking you if you could offer a lottery-like option to them. The option is summarized as
below. What would be the option price using the binomial tree model?
At maturity,
– If the unit digit of the stock is an odd number, pay $1
– If the unit digit of the stock is an even number, pay $2
– If the tens digit of the stock is identical to its unit digit, pay additional $5. (If the stock price at
maturity is less than 10, the tens digit is zero.)
= 100 with volatility = 25% where continuously compounded risk free rate is = 0.15%. Suppose
an option with maturity = 0.5 and = 125 time steps between = 0 and = . Hence, each time
increment is =
0.5
125
. The stock pays no dividends.
Complete and fix the FUNCTION named ‘task3’ in the module ‘Q3’. You may want to reuse a triangular
matrix used in task 2 while amending the option pay-off at maturity.