In problems 1 and 2; I want you to find the theoretical price of a call and a put using B-S model. To do this; you need to use a software. There are plenty of free access softwares in internet. So you can use one of them for the calculation of theoretical call and put premium values on the basis of B-S. The options in my questions are European options. Due to format differences, it is possible that different softwares give slightly different answers. I will accept answers which are reasonably close to the ones that I find as valid. If you want; you can also mention the name of the software which you used in your answer though this is not a requirement. 1) What is the B-S value of a European call if S=20,K=22;T=1 month (use either 30 days or 0.083 years); expected volatility =30% and interest rate =10% ? (20pts) 2) What is the BS value of a European put if S=36,K=40;T=3 months; Expected Volatility =18% and r=1% ? What is the intrinsic value and the time value of that put? ( 20pts) 3) An investment fund who holds 100000 shares of ABC stock wants to hedge the position assuming that the current price of 80 may go down by buying put contracts written on that stock. The puts that will be bought has a remaining maturity of 3 months and an exercise price of 80. How many put contracts must be bought for a possible perfect hedge if the delta of put is -0.5 and contract multiplier of the put is 100 shares? (20 pts) 4) A European call option where S=16,K=15,T=0.25,r=1% and Vol =25% has a current B-S value of $1.39 per share. This call also sells in the market at the value of $139. The vega is 2.66 and the theta is 1.435. Given that a) What may be the total premium if Vol goes up to 28% under ceteris paribus assumptions? ( 10pts) b) What may be the total premium after 4 days under ceteris paribus assumptions? (10 pts)? 5) In the problem above in which the BS value for premium is $139; assume that the market value of premium is $146. Apparently there is an arbitrage possibility. What you must do to have an arbitrage gain? Assuming that you implement arbitrage by 1000 calls; what may be your arbitrage gain? (20 pts.) In problems 1 and 2; I want you to find the theoretical price of a call and a put using B-S model. To do this; you need to use a software. There are plenty of free access softwares in internet. So you can use one of them for the calculation of theoretical call and put premium values on the basis of B-S. The options in my questions are European options. Due to format differences, it is possible that different softwares give slightly different answers. I will accept answers which are reasonably close to the ones that I find as valid. If you want; you can also mention the name of the software which you used in your answer though this is not a requirement. 1) What is the B-S value of a European call if S=20,K=22;T=1 month (use either 30 days or 0.083 years); expected volatility =30% and interest rate =10% ? (20pts) 2) What is the BS value of a European put if S=36,K=40;T=3 months; Expected Volatility =18% and r=1% ? What is the intrinsic value and the time value of that put? ( 20pts) 3) An investment fund who holds 100000 shares of ABC stock wants to hedge the position assuming that the current price of 80 may go down by buying put contracts written on that stock. The puts that will be bought has a remaining maturity of 3 months and an exercise price of 80. How many put contracts must be bought for a possible perfect hedge if the delta of put is -0.5 and contract multiplier of the put is 100 shares? (20 pts) 4) A European call option where S=16,K=15,T=0.25,r=1% and Vol =25% has a current B-S value of $1.39 per share. This call also sells in the market at the value of $139. The vega is 2.66 and the theta is 1.435. Given that a) What may be the total premium if Vol goes up to 28% under ceteris paribus assumptions? ( 10pts) b) What may be the total premium after 4 days under ceteris paribus assumptions? (10 pts)? 5) In the problem above in which the BS value for premium is $139; assume that the market value of premium is $146. Apparently there is an arbitrage possibility. What you must do to have an arbitrage gain? Assuming that you implement arbitrage by 1000 calls; what may be your arbitrage gain? (20 pts.)
