# Scaling Stock Price and Strike etc. by a Constant

Please provide steps to justify the below.

1) If the stock prices, strike and other price related parameters are scaled by the same constant, will the derivative price scale accordingly? I would think this is different from using a constant as a numeraire, since a numeriance does not affect the strike price. Please confirm.

2) Would scaling by a constant lead to any issues (or a different price), when pricing vanilla options?

3) Are there any derivatives (exotics) whose price is affected when scaling by a constant? One example, is a variance swap as suggested by user @Mats Lind

Related Question: Using a Constant as a Numeraire

The rest of standard Geometric Brownian Motion and Black Scholes assumptions apply.

• For question 1), it depends on the payoff format. For example, $(aS_T-aK)^+=a(S_T-K)^+$, the price is also changed. On the other hand $(aS_T/(aK)-1)^+=(S_T / K-1)^+$, the price will not change. – Gordon Aug 17 '16 at 15:01