14 May EXPLAIN HOW YOU WOULD USE A BINOMIAL TREE TO PRICE THIS OPTION.
What has higher value for options of strike K that are
at-the-money at inception:
(a)
A cliquet option with maturity T = 1 year and a single reset at T
= 1=2 year?
(b)
A one-shout shout option with maturity T = 1 year?
26.
(Requires Writing Code) (a) Write a program to price a down-and-in
barrier call option with the following parameters: S = 50, strike K = 50, an
annual risk-free rate r = 3%, volatility = 0:3, and barrier H = 45. Use a CRR
pricing tree with a time step of one year for each period. The maturity of the
option is six years.
(b)
Modify the program to price the down-and-in put.
(c)
Does European put-call parity hold for barrier options? Why?
27.
(a) Price a ten-year down-and-in
barrier call option with the following parameters: S = 100, strike K = 102,
annual risk-free rate r = 2%, volatility = 0:4, and barrier H = 90. Use a time
step of one year on the CRR tree for this problem.
(b)
Price the down-and-out barrier call with the same parameters.
Sundaram
& Das: Derivatives – Problems and Solutions . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . 295
(c)
Price the vanilla call with the same parameters.
(d) Verify that the sum of the prices you obtain in parts (a) and (b)
equals the price you obtain in part (c).
28. Consider a shout option with strike K. One way to price the
option is as follows. If at some point in time prior to maturity, you shout
when the stock price is S > K, then you capture the pro ts S K (to be paid
at maturity) and the original shout call option held is replaced with a new
vanilla call option with a strike of S for the remaining maturity.
(a)
Explain how you would use a binomial tree to price this option.
(b) Will the tree be recombining? That is, can the option be priced by
backwards recursion?
(c)
Is the option path-dependent?.
29. Price a ten-year Asian
option with an initial stock price of $50, strike $50, annual risk-free rate r
= 10%, and volatility = 0:35. Price the call and the put, and see whether
put-call parity holds. Use a pricing tree with a time step of one year per
period.
30. (Requires Writing Code) For the same parameters as in the previous
question, price a lookback price call and put.
31. (Requires Writing Code) Implement the formula in the chapter
appendix for up-and-out calls, and value the option for the following
parameters: S = 102, K = 100, r = 5% p.a., barrier H = 130, and maturity T =
0:25. Annualized volatility is = 40%.
Sundaram
& Das: Derivatives – Problems and Solutions . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . 298
Program a tree model to do the same and report the value. Compare
the tree model to the closed-form answer.
.
32. In the preceding question, what is the e ect of increasing the
maturity of the up-and-out call? Keep the parameters the same but vary the
maturity to take the following values (in years): 0.1, 0.2, 0.3, 0.5, and 1.0.
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