Assume the date is 25 February 2021. The Korean Composite Stock Price Index, or KOSPI, closed at
Assume the date is 25 February 2021. The Korean Composite Stock Price Index, or KOSPI, closed at 3100. The one-year risk-free rate for the Korean won is 0.8025%. KOSPI is expected to pay a dividend yield of 2% and the ex-dividend date is the 18 August 2021. The volatility of KOSPI on the same day is 27.92%. The head of structuring asks for your help with the knock-in put of the auto callable with a barrier of H. Assume a day count convention of 360 days, a cash rebate of 0 for exotics, and the expiration date for all exotics is 20 February 2022.
a) Explain what a down-and-in European barrier put option is. Can it be replicated by a set of more basic option contracts? If yes, how? If not, why not?
b) Using 10-step binomial tree and the Cox-Rubinstein-Ross parameterisation, price an at-the-money (ATM) European down-and-in put with barrier (HL) set at the index level of 2900.
c) Using the Binomial tree prices obtained in part b, plot and discuss the P&L of the short ATM European down-and-in put option with the barrier HL= 2900.
d) Using the Black-Scholes model, price the vanilla equivalent with the same contractual characteristics. What drives the differences between the two prices derived here and in part b? How can the two option price solutions converge?
Any calculations for these questions should be done in excel and show formulas you use.