def Delta(self, tp, cp):
# if the option is EUROPEAN we have a closed formula
if tp == "E" or (cp == "Call" and self.q == 0):
x = np.append(np.linspace(self.S / 100, self.S * 2.5, 1000),
np.array([self.S]))
# call formula
if cp == "Call":
y = np.exp(-self.q * self.t) * norm.cdf(self.d1(x))
# put formula
elif cp == "Put":
y = -np.exp(-self.q * self.t) * norm.cdf(-self.d1(x))
return (plot(x[:-1], y[:-1], "Delta", "", ""), y[-1])
# if the option is AMERICAN we use the central difference estimator
elif tp == "A":
x = np.linspace(self.S / 100, self.S * 2.5, 1000)
h = x[1] - x[0]
values = np.array([
binomial_model(u, self.K, self.t, 0, self.q, self.r, self.s,
50, "American", cp) for u in x
])
delta = np.array([(values[i + 2] - values[i]) / (2 * h)
for i in range(values.size - 2)])
x = x[1:len(x) - 1]
delta_curr = binomial_model(self.S + h, self.K, self.t, 0, self.q,
self.r, self.s, 50, "American", cp)
delta_curr -= binomial_model(self.S - h, self.K, self.t, 0, self.q,
self.r, self.s, 50, "American", cp)
delta_curr /= 2 * h
return (plot(x[:-1], delta[:-1], "Delta", "", ""), delta_curr)
def Theta(self, tp, cp):
x = np.append(np.linspace(self.S / 100, self.S * 2.5, 1000),
np.array([self.S]))
if tp == "E" or (cp == "Call" and self.q == 0):
if cp == "Call":
y = -np.exp(-self.q * self.t) * x * norm.pdf(
self.d1(x)) * self.s / (2 * np.sqrt(self.t))
y -= self.r * self.K * np.exp(-self.r * self.t) * norm.cdf(
self.d2(x))
y += self.q * x * np.exp(-self.q * self.t) * norm.cdf(
self.d1(x))
y /= 252
elif cp == "Put":
y = -np.exp(-self.q * self.t) * x * norm.pdf(
-self.d1(x)) * self.s / (2 * np.sqrt(self.t))
y += self.r * self.K * np.exp(
-self.r * self.t) * norm.cdf(-self.d2(x))
y -= self.q * x * np.exp(
-self.q * self.t) * norm.cdf(-self.d1(x))
y /= 252
return (plot(x[:-1], y[:-1], "Theta", "", ""), y[-1])
elif tp == "A":
h = 0.001
theta = np.array(
[(binomial_model(u, self.K, self.t - h, 0, self.q, self.r,
self.s, 50, "American", cp) -
binomial_model(u, self.K, self.t + h, 0, self.q, self.r,
self.s, 50, "American", cp)) / (2 * h)
for u in x]) / 252
return (plot(x[:-1], theta[:-1], "Theta", "", ""), theta[-1])
def Vega(self, tp, cp):
x = np.append(np.linspace(self.S / 100, self.S * 2.5, 1000),
np.array([self.S]))
if tp == "E" or (cp == "Call" and self.q == 0):
y = 0.01 * x * np.exp(-self.q * self.t) * np.sqrt(
self.t) * norm.pdf(self.d1(x))
return (plot(x[:-1], y[:-1], "Vega", "", ""), y[-1])
elif tp == "A":
h = 0.001
vega = 0.01 * np.array(
[(binomial_model(u, self.K, self.t, 0, self.q, self.r,
self.s + h, 50, "American", cp) -
binomial_model(u, self.K, self.t, 0, self.q, self.r,
self.s - h, 50, "American", cp)) / (2 * h)
for u in x])
return (plot(x[:-1], vega[:-1], "Vega", "", ""), vega[-1])
def Rho(self, tp, cp):
x = np.append(np.linspace(self.S / 100, self.S * 2.5, 1000),
np.array([self.S]))
if tp == "E" or (cp == "Call" and self.q == 0):
if cp == "Call":
y = 0.01 * self.K * self.t * np.exp(
-self.r * self.t) * norm.cdf(self.d2(x))
elif cp == "Put":
y = 0.01 * -self.K * self.t * np.exp(
-self.r * self.t) * norm.cdf(-self.d2(x))
return (plot(x[:-1], y[:-1], "Rho", "", ""), y[-1])
elif tp == "A":
# the plot will be Rho on the y axis and S on the x axis
# therefore we calculate the derivative with respect to r
# for each value of S (this is done also in the other greeks)
h = 0.001
rho = 0.01 * np.array(
[(binomial_model(u, self.K, self.t, 0, self.q, self.r + h,
self.s, 50, "American", cp) -
binomial_model(u, self.K, self.t, 0, self.q, self.r - h,
self.s, 50, "American", cp)) / (2 * h)
for u in x])
return (plot(x[:-1], rho[:-1], "Rho", "", ""), rho[-1])
def Gamma(self, tp, cp):
if tp == "E" or (cp == "Call" and self.q == 0):
x = np.append(np.linspace(self.S / 100, self.S * 2.5, 1000),
np.array([self.S]))
# here we don't need two formulas since gamma is the same for calls and puts
y = np.exp(-self.q * self.t) * norm.pdf(
self.d1(x)) / (x * self.s * np.sqrt(self.t))
return (plot(x[:-1], y[:-1], "Gamma", "", ""), y[-1])
elif tp == "A":
x = np.linspace(self.S / 100, self.S * 2.5, 1000)
h = x[1] - x[0]
values = np.array([
binomial_model(u, self.K, self.t, 0, self.q, self.r, self.s,
50, "American", cp) for u in x
])
delta = np.array([(values[i + 2] - values[i]) / (2 * h)
for i in range(values.size - 2)])
gamma = np.array([(delta[i + 2] - delta[i]) / (2 * h)
for i in range(delta.size - 2)])
x = x[2:len(x) - 2]
delta_curr = binomial_model(self.S + h, self.K, self.t, 0, self.q,
self.r, self.s, 50, "American", cp)
delta_curr -= binomial_model(self.S - h, self.K, self.t, 0, self.q,
self.r, self.s, 50, "American", cp)
delta_curr /= 2 * h
delta_curr_2 = binomial_model(self.S + (2 * h), self.K, self.t, 0,
self.q, self.r, self.s, 50,
"American", cp)
delta_curr_2 -= binomial_model(self.S, self.K, self.t, 0, self.q,
self.r, self.s, 50, "American", cp)
delta_curr_2 /= 2 * h
gamma_curr = (delta_curr_2 - delta_curr) / (2 * h)
return (plot(x[:-1], gamma[:-1], "Gamma", "", ""), gamma_curr)