Features of an option that affect its market value

[archived_user]

I understand which factors affect the value of an option, but I am a bit confused as to this question I came across.
In each of the following questions, you are asked to compare two options with parameters as given. The risk-free interest rate for all cases should be assumed to be 6%. Assume the stocks on which these options are written pay no dividends.
Put T X s Price of Option
A .5 50 .20 10
B .5 50 .25 10
Which put option is written on the stock with the lower price?
1. A
2. B
I understand obviously the volatility differs with put A and put B. But I think I am not understanding the question.

 

[archived_user]

Both options have the same price (the premium), yet the volatility of the put option on stock B is higher. What other factor is at play here? That’s the price of the underlying, the stock.The question is asking which put option is written on the stock with the lower price. If stock A and B would have the same price, the option price of B should be higher given the higher volatility. As the stock price increases, the value of a the put option decreases because it’s less likely to be in-the-money. This implies that the price of stock B is higher than stock A, since the higher volatility of B is offsetting the higher price of B. Thus the stock with the lower price is A.

 

[archived_user]

That makes perfect sense.
If the question were to change to that of a call so that:
Call T X S Price of Option
A .5 50 55 10
B .5 55 55 7
Which call option on the stock is written with the higher volatility?
A
B
Or is there too little information?

 

[archived_user]

I’d say there is too little information to determine which stock has the higher volatility. Both strike price and option price are different. Lower strike price of a call option increases its value. To me it’s unclear whether the price of $10 for option A is driven by its volatility or lower strike price relative to option B. In this case I’d be asking myself the question: what would the option price be if both options had the same strike price?

 

[archived_user]

Thanks Moonborne. That makes perfect sense