# Calculate strike from Black Scholes delta

I have a list of deltas and their corresponding volatilities in an FX market but I want to go from delta to strike price. In this Question similar problem is being discussed

How can I calculate the strike price or implied volatility from a given delta?

The way I understand it, the strike price can be found like this: Is my approach correct? If yes; pleace help me understand the term, N(d_1), so I can proceed with the solve process?

Edit:
I basically want to create the volatility smile in (strike,vol)-graph from data found by Bloombergs OVDV function: So maybe there's a simplere way to do so

• In Excel the function N(d1) is called NORMSDIST(). In many other languages there is such a function. In Python it;s norm.cdf() as part of Scipy. – noob2 Aug 5 '16 at 19:36
• In R; is it dnorm() og pnorm()? – Sanjay Aug 5 '16 at 19:38
• It's pnorm() in R language. It's a "p" because it returns a probability (a number between 0 and 1). – noob2 Aug 5 '16 at 19:43

Most pairs take premium in the foreign (i.e. left hand side) currency. This means that you are paying for an option in the underlying - like paying for an IBM call option with IBM shares - and those shares can be viewed as part of the delta - as a result most pairs use the "include premium" convention. The details are in Wystup's paper and you should read it. The math is easy and it is nice to see everytrhing spelled out for you. The only pairs that "Exclude Premium" are EURUSD, GBPUSD, AUDUSD, NZDUSD - so these calculate delta in the usual way. Also in FX for BBG, the convention is to typically use spot delta for expiries less than a year and forward delta for expiries >= 1 year. Otherwise onlyvix's answer above is fine if you assume that the foreign risk free rate is 0.0%. The actual delta is $e^{-r_ft}N(d1)$ in the exclude premium case.
• Thanks, @FinanceGuyThatCantCode. I am struggling with the Time parameter. It makes a huge difference whether I use days, months etc. If I use $T=1/12$ (years) for the 1 month options I get my points really really close the ATM than if I use $T=21$ (days). By looking at the example provided above, What's the correct way of measuring time $T$ – Sanjay May 22 '17 at 13:37
• So, for for 1 month option, the the time $T$ is approximately $T=(30/365)$ ? I am not sure if I have understood it correctly. – Sanjay May 22 '17 at 17:25
Since $\Delta_K = N(d_1)$ use normal inverse function $N^{-1}$ (e.g. NORM.INV in excel, norminv in matlab) to calculate $d_1 = N^{-1} (\Delta_K)$ Then use algebra to solve for $K$