# 1. Each student will choose a unique company for this assignment – I have created a Discussion Board in Canvas – on which you have to post the name of the company you are choosing – first posted...

1. Each student will choose a unique company for this assignment – I have created a Discussion Board in Canvas – on which you have to post the name of the company you are choosing – first posted student gets it – everyone else has to choose some OTHER company. The ONLY company you cannot choose is GOOG – which I am using as an example firm.

Get a quote (mention date/time on your submission) of a Call and a Put for the SAME X & T. Use the quotes to show what the Implied Volatility (IV) is of your chosen stock and whether the Put Call Parity holds or is violated by your quotes. IF the put-call parity is NOT maintained, then what would be the possible arbitrage opportunity you have found (how to profit from it)? (20 pts)

The company I chose was Target corporation

## Solution

Prateek answered on Apr 16 2022
Black & Scholes
VALUING A LONG TERM OPTION - WITH DIVIDEND ADJUSTMENT
This program calculates the value of a long term option (> 1 year)                                    Based on Vesting Schedule    Maximum
adjusting for dividends using the expected dividend                                    Vesting Period (Days)    27            Liquidity Event
yield on the cu
ent value of the asset.                                    Average    27            Investor Induction    2    years
Assumed Exercise Period     0.07            IPO    5    years
Assumptions                                                Others
1. All the assumptions underlying the Black-Scholes model apply
2. The dividend yield over the lifetime of the option is known and a constant.
The user has to input the following variables
1. Cu
ent market value of the underlying asset
2. Variance in the ln(value) of the underlying asset
3. Strike price of the option
4. Riskless interest rate that co
esponds to the life of the option                                Cu
ent Stock Price
5. Time to expiration on the option
6. Expected dividend yield on the underlying asset.
Inputs relating the underlying asset
Enter the cu
ent market value of the underlying asset =                    237
Enter the annualized standard deviation in ln(value) of asset                    31.43%    (in %)
Enter the cu
ent annualized dividends on the asset                    0.00    (in cu
ency)
This will result in a dividend yield of                    0.00%
Do you want to change this dividend yield for the life of the option?                    No    (Yes or No)
If yes, enter the new dividend yield for the life of the option =                        (in %)
Inputs relating to the option
Enter the strike price on the option =                    210    (in cu
ency)
Enter the time to expiration on the option (in years) =                    0.07    (in years)
General Inputs                                T-Bill Rate
Enter the riskless rate that co
esponds to the option lifetime =                    5.53%    (in %)
VALUING A LONG TERM OPTION/WARRANT
Stock Price        237        T.Bond rate        2.83%
Strike Price        210        Variance        0.10
Expiration (in years)        0.0739726027        Annualized dividend yield        0.00%
Working for Call Option
d1    1.49
N(d1)    0.93
d2    1.41
N(d2)    0.92
Value of the call    28.27
Call Value in Market    28.05    Target Corporation Common Stock (TGT) Option Chain | Nasdaq    Check out the last one in this link for Call
Value of the put     1
Put Value in Market    1    Target Corporation Common Stock (TGT) Option Chain | Nasdaq    Check out the last one in this link for Put
Put Call Parity
LHS    RHS
238    238
Here, it can be seen that the put-call parity of the stock holds wherein the sum of the stock price and the put option value is equal to the sum of strike price and the value of the call option. Thus, there is no a
itrage opportunity available. Further, this can be justified by the fact that the value of the call and the put option is very similar to the ones in the market. Thus, no a
itrage opportunity is there.
https:
www.nasdaq.com/market-activity/stocks/tgt/option-chainhttps:
www.nasdaq.com/market-activity/stocks/tgt/option-chain
Volatility
Date    Target Corporation...
SOLUTION.PDF