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Asian Options

So far, we dealt with options where the payoff depends only on the final price of the stock:

  • Call \(max(S_T - K,0)\)
  • Put \(max(K-S_T,0)\)

But path-dependent options are different. Their payoff depends on the entire path the stock price takes - not just the final value.

Its like saying: “I care not just about where you are now, but everywehre you’ve been before you got here”

Examples of Path-dependent options

  1. Asian Option: Payoff depends on the average price of the underlying asset during the life of the option.
    1. Asian Call: \(max(\bar S - K,0)\)
    2. Asian Put: \(max(K-\bar S,0)\)
  2. Lookback Option: Payoff depends on the maximum or minimum stock price during the life of the operation.
  3. Barrier Option: Payoff activates only if a price hits a barrier at some point in time.

Asian Option with Binary Tree

wqu supports building and checking the Asian (european style exercise only) with Python:

Python
from wqu.dp import BinomialTree


bt_asian = BinomialTree(
    S0=100, K=95, T=1, r=0.05,
    u=1.1, d=0.9, N=3,
    option_type='call',
    option_style='asian'
)

bt_asian.build_stock_tree()
bt_asian.build_option_tree()
print("Asian Call Price:", bt_asian.price())