Fin47

Finance Assignment Help 47

 
Explain if there is arbitrage in this equation.
Written part
 
1) Assume for a non dividend paying stock So= 80, vol= 30% p.a, r= 3% pa.cc, time= 9 months.

{40 if St <=70
{100 – St, If 70<St<110
{0.        Otherwise

In R (program)

a- Value x, early exercise ->E style option not allowed. 250 step C-R-R binomial tree
* Value= 25.85 -> How?
 
b- Can x be created by combination of bond (face value 40) short call at strike 70 and long call at strike 110? Explain
 

                  St<=7070<St<=110St>100
Bond.       40             40                 40
SC70         0             70(k)-St       70- St
LC110       0                  0                St – 110
                 40               110-St            0

 
If you price separately EC70= 14.78 EC110= 1.52
39.11-14.78+1.52= 25.85 -> price of x
 
c- Show x can be created by only 2 EP options separately by using binomial tree
 
d- Value the 2 option with 250 steps. Show that the portfolio of these 2 options has the same value as X
 
 

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2) Excel
 
a- 3 months “down and in” call option N-D paying stock, Stock price= 100, Strike price =100, rf= 8%, vol=30% pa, barrier 95, time intervals= 200, 500 simulations.
 
b- Calculate the 95% confidence interval of the option price.
 
3) 12 months Bermudian style put option N-D paying stock
Stock price =100, Strike price= 100, rf=3% pa.cc, vol= 30% pa. Early exercise on first day of 3rd, 6th and 9th month.
 
a- 252 day in one year. Price the option. 100 step binomial tree.
 
b- 2% dividend yield pa.cc on the stock?
 
4) Theory question – S follows a process dS= mSdt + oSdz where m and o are constant. What is the probability followed by Y=. If S follows a process dS= k (b-S) dt + oSdz where k, b, o are constant. What’s the process followed by Y =?
 
5) 12 months, EC option N-D paying stock , rf= 3% pa.cc, vol= 30% pa
 

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