0
$\begingroup$

I want to know the probability that the strike price of an option is touched. My input values are:

P = price
S = strike
v = vol
t = time to expiration

According to the answer of Hans in the following topic, the probability of touching a barrier when the underlying has zero drift is equal to:

$0.5 * (1-\text{erf}\Big(\frac{x}{\sqrt 2}\Big))$

How can I rewrite x in terms of my input values?

$\endgroup$
0
$\begingroup$

There should be a factor of a half in front. No? $$x = \frac{S-P}{vol \sqrt{t}}$$

| improve this answer | |
$\endgroup$
  • $\begingroup$ agreed, but is x the same as d1 for normal BS formula? $\endgroup$ – HJA24 May 26 at 19:02
  • $\begingroup$ @HJA24 The cumulative normal distribution evaluated at that point is the probability that the price will end up at or above the strike. $\endgroup$ – stackoverblown May 26 at 20:11
  • $\begingroup$ The function erf() in your formula can (if you want) be converted to the function N() used in Black Scholes using a well known identity. Most Finance people use N(), mathematicians like erf(). $\endgroup$ – noob2 May 26 at 20:20
  • $\begingroup$ @stackoverblown okay, but I want the probability that it touches the strike at some point in time, not solely on the expiration date $\endgroup$ – HJA24 May 27 at 9:06
  • $\begingroup$ @HJA24 Which will be the one minus the probability that the stock price never reaches the strike price at any point up to expiry. $\endgroup$ – stackoverblown May 27 at 17:30

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.