fat_tails_and_their_impact_on_option_prices3

8a26dfa7-fdb4-4ced-885f-dd447723634a.py

# set stock params
spot = 100
sigma = 0.20
n = 10000
# option strikes
ks = np.linspace(65, 165, 21)
eps = [0, 0.3, 0.6, 0.85]

# compute closing prices
pxs = {}
op_pxs = {}
for e in eps:
    # init distribution class
    dist = cust_dist(e=e)
    # sample returns from dist
    rets = sigma * dist.rvs(size=n)
    # compute prices
    px = spot * np.exp(rets)
    # add pxs to price dict
    pxs[e] = px
    # compute option pxs
    op_px = [np.mean([max(x - k, 0) if k > spot else max(k - x, 0) for x in px]) for k in ks]
    # add to option price dict
    op_pxs[e] = op_px

# plot them
fig, ax = plt.subplots(figsize=(25,10))

for e, op_px in op_pxs.items():
    ax.plot(ks, op_px, label="e = {}".format(e))

ax.set_title("Time Value for Various Option Strikes", fontsize=24)
ax.set_xlabel("Option Strike, K", fontsize=20)
ax.set_ylabel("Time Value", fontsize=20)
ax.legend(fontsize=14);