MATLAB - implied volatility

In summary, the MATLAB function newt_iv uses Newton's method to find the root of the difference between the actual call price and the Black-Scholes call price, solving for implied volatility. However, if the slope is zero, the function may return incorrect values. To address this issue, a check for the value of the slope can be added and the loop can be exited if the slope is zero.
  • #1
mts_88
1
0
I have found the following function for calculating implied volatility in MATLAB.
When it finds a solution, the solution tends to be correct, but the function does not take into account, that the slope can be zero. If this happens, you divide by zero and the function return inf or -inf, which isn't correct at all. I have tried to take this problem into account, but the result is that the function does not converge. Does anyone have an idea how to implement this in the function?

Matlab:
% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %
% -------------------------------------------------------------------
% NEWT_IV.M
% -------------------------------------------------------------------
% The function uses Newton's method to find the root of
% the actual call price minus the Black-Scholes call price, solving
% for volatility.
% -------------------------------------------------------------------
% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %

% FUNCTION: newt_iv
% Input(s):
% - C: actual call price expressed in home currency
% - S: price of the underlying expressed in home currency
% - K: strike price of the underlying expressed in home currency
% - r: risk-free rate expressed as a decimal (5%=0.05)
% - T: Tenor expressed in years (6 months=0.5)
% Output(s): the approximate implied volatility using Black-Scholes
% and Newton's method. The approximated implied volatility and
% number of iterations taken to achieve an accurate result are
% displayed.
%
function ivol = newt_iv(C,S,K,r,T)

% Anonymous functions for Black-Scholes
d1 = @(S,K,r,vol,T) (log(S/K)+(r+vol^2/2)*T)/(vol*sqrt(T));
d2 = @(S,K,r,vol,T) d1(S,K,r,vol,T)-vol*sqrt(T);
bscp = @(S,K,r,vol,T) S*normcdf(d1(S,K,r,vol,T),0,1)-K*exp(-r*T)*normcdf(d2(S,K,r,vol,T),0,1);
vega = @(S,K,r,vol,T)S*normpdf(d1(S,K,r,vol,T),0,1)*sqrt(T);
% Initial guess
ivol = 0.2;

% Error tolerance
err = 0.0001;

% Set a limit to the number of iterations
i = 1; % number of iterations
ilimit = 2000000; % limit

cpdiff = err+1; % Cause the first iteration to occur (see next line)
while abs(cpdiff) > err
% Terminate the algorithm if the iteration limit has been reached
if (i > ilimit)
str = sprintf('ERROR: Implied volatility could not be found after %d iterations.', ilimit);
disp(str);
ivol = inf;
break;
% Otherwise continue the iteration
else
i = i+1;
end

% Calculate Black-Scholes call price for current implied
% volatility guess.
ccprice = bscp(S,K,r,ivol,T);

% Find the difference between calculated call price and
% actual call price.
cpdiff = ccprice - C;

% If the calculated call price minus the actual call price is not
% small enough, adjust the guess using Newton's method
if abs(cpdiff) > err
slope = vega(S,K,r,ivol,T);
y_int = cpdiff-slope*ivol;
ivol = -y_int/slope;
end
% If the calculated call price minus the actual call price is zero,
% a root as been found. Unless a root as been round, repeat
% the process using the new upper and lower bounds.
end
ivol;
end
 
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  • #2
I think the best way to implement this in the function is to add a check for the value of the slope. If the slope is zero, then the implied volatility can be set to the current guess and the loop can be exited. This should allow the algorithm to converge without dividing by zero.
 

1. What is implied volatility in MATLAB?

Implied volatility in MATLAB is a measure of the expected volatility of a financial instrument, such as a stock or option, based on the prices of its options contracts. It is calculated using the Black-Scholes model and is a key factor in pricing options and making investment decisions.

2. How is implied volatility calculated in MATLAB?

Implied volatility is calculated in MATLAB using the "blsimpv" function, which takes in the current price of the underlying asset, strike price, time to expiration, interest rate, and option price. It uses the Black-Scholes model to solve for the implied volatility, which is then returned as a percentage.

3. How does implied volatility affect options pricing in MATLAB?

In MATLAB, implied volatility has a direct impact on the pricing of options contracts. Higher implied volatility results in higher option prices, as there is a higher expected risk associated with the underlying asset. Conversely, lower implied volatility leads to lower option prices.

4. Can implied volatility be used to predict future stock prices in MATLAB?

No, implied volatility cannot be used to predict future stock prices in MATLAB or any other programming language. It is a measure of expected volatility and does not take into account other factors that can affect stock prices, such as market trends and company performance.

5. How can implied volatility be used in MATLAB for risk management?

Implied volatility can be used in MATLAB for risk management by helping investors and traders determine the level of risk associated with their options positions. By understanding the implied volatility of an option, they can make more informed decisions about their investments and manage their risk accordingly.

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