Assignment 2
unity代做 – 这个题目属于一个unity的代写任务, 是比较有代表性的unity等代写方向
Question 1
Based on the put-call parity, the value of protective put should be equal to that of fiduciary call if there are no arbitrage opportunities. However, based on the parameter given above, the value of protective put is $120+$8=$128, while the value of fiduciary call is $119e^(-4%0.5)+$ 12 =$128.6436 if keeping four decimals. There is a difference between these two, so there is an arbitrage opport unity and the difference of $128.6436-$128=$0.6436 can be made as profit risk-freely. To achieve this, the following steps would need to be taken:
a) At the time of portfolio set-up, the investor sells one unit call option with a strike price of
$ 119 maturing after half year to get the premium $ 12.
b) To replicate the call option, the investor also buys a put option with a strike price of $ 119
maturing after half year by paying $ 8 and a share of underlying stock at $120. In addition, the
investor needs to sell a zero-coupon bond with face value of $119 which matures in half year
with interest rate of 4%, compounded continuously. The investor would need to spend
$8+$120-$119*e^(-4%*0.5)=$ 11.
c) By doing this, the investor can gain risk-free profits of $12-$11.3464=$0.6436.
Question 2
As there is no arbitrage opportunity, the current price of put option should be based on the intrinsic value of the put option discounted by interest rate.
=( )!"$
Forward Price = $120, T= 6 /12 =0.5 years, r = 5% and put option price = $14.63. By plugging these parameters into the equation, we have:
$14. 63 =( $120)!%%’.%
By solving this equation, we can obtain the strike price K = $135.0004. Therefore, the highest possible strike price is $135.000 4
Question 3
The price of a European call on the stock is $4.0963 while the price of a European put is $3.8371.
variations in the stock price
As shown in the chart above, the call option price increases when stock price increases while the put option price decreases when stock price increases. This can be explained by the nature of the option, as the value of call option is the max(stock price-strike price,0), the higher stock price, the higher intrinsic value of the call option.
Variation in the risk-free interest rate
As shown above, the call option price increases with higher interest rate while the put option price
decreases. With an increase in interest rate, shorting stock becomes more profitable than buying puts as
the former generates income and the latter does not, so put option prices are impacted negatively by increasing interest rates. However, an increase in call option would lead more saving into loans and the call option would be more profitable and thus its price increases.
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404142434445464748495051525354555657585960
variation in stock price
call put
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0.030.0320.0340.0360.0380.040.0420.0440.0460.0480.050.0520.0540.0560.0580.060.0620.0640.0660.0680.
variation in risk-free interest rate
call put
Variation in time to maturity
Both the call option price and put option price would increase with longer maturity. As the value of option is the sum of intrinsic value and time value, the option value would be larger with longer time to maturity as time value increases. At six month, a dividend would be issued and thus making the changes above.
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0.30.320.340.360.380.40.420.440.460.480.50.520.540.560.580.60.620.640.660.680.
Variation in Time to Maturity
call put