# Wolfram Language™

## Find the Value of a European Call Option

Find the value of a European vanilla call option if the underlying asset price and the strike price are both \$100, the risk-free rate is 6%, the volatility of the underlying asset is 20%, and the maturity period is 1 year, using the BlackScholes model.

In[1]:=
```TraditionalForm[BlackScholesModel = {-(r c[t, s]) + r s \!\( \*SubscriptBox[\(\[PartialD]\), \({s}\)]\(c[t, s]\)\) + 1/2 s^2 \[Sigma]^2 \!\( \*SubscriptBox[\(\[PartialD]\), \({s, 2}\)]\(c[t, s]\)\) + \!\( \*SubscriptBox[\(\[PartialD]\), \({t}\)]\(c[t, s]\)\) == 0, c[T, s] == Max[s - k, 0]}]```

Solve the boundary value problem.

In[2]:=
```(dsol = c[t, s] /. DSolve[BlackScholesModel, c[t, s], {t, s}][[ 1]]) // TraditionalForm```

Compute the value of the European vanilla option.

In[3]:=
```dsol /. {t -> 0, s -> 100, k -> 100, \[Sigma] -> 0.2, T -> 1, r -> 0.06}```
Out[3]=

Compare with the value given by FinancialDerivative.

In[4]:=
```FinancialDerivative[{"European", "Call"}, {"StrikePrice" -> 100.00, "Expiration" -> 1}, {"InterestRate" -> 0.06, "Volatility" -> 0.2 , "CurrentPrice" -> 100}]```
Out[4]=