# EuropeanBinomPut_ImpVol#

## Purpose#

Computes implied volatilities for European put options using binomial method.

## Format#

sigma = EuropeanBinomPut_ImpVol(p, S0, K, r, div, tau, N)#
Parameters:
• p (Mx1 vector) – put premiums.

• S0 (scalar) – current price.

• K (Mx1 vector) – strike prices.

• r (scalar) – risk free rate.

• div (scalar) – continuous dividend yield.

• tau (scalar) – elapsed time to exercise in annualized days of trading.

• N (scalar) – number of time segments. A higher number of time segments will increase accuracy at the expense of increased computation time.

Returns:

sigma (Mx1 vector) – volatility.

## Examples#

```// Specify put premiums
p = { 14.60, 17.10, 20.10 };

// Specify current price
S0 = 718.46;

// Specify strike prices
K = { 720, 725, 730 };

// Specify risk free rate
r = .0398;

// Specify dividend
div = 0;

// Specify start and end dates
t_start = dtday(2012, 1, 30);
t_end = dtday(2012, 2, 16);

// Find annualize elapsed trading days

// Compute volatility
sigma = EuropeanBinomPut_ImpVol(p, S0, K, r, div, tau, 30);
print sigma;
```

produces:

```0.21609253
0.21139494
0.21407512
```

## Remarks#

The binomial method of Cox, Ross, and Rubinstein (“Option pricing: a simplified approach”, Journal of Financial Economics, 7:229:264) as described in Options, Futures, and other Derivatives by John C. Hull is the basis of this procedure.

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