Discrete Delta Hedging and Its Convergence

Summary

The document asks for rigorous references on implementing discrete delta hedging. Its starting example is a call option hedged by holding the option’s delta in the underlying stock, with the bank account adjusted to keep the portfolio self-financing. The author is interested in how this strategy behaves when hedges are updated at discrete times, including convergence, optimal hedge choices, and applications to exotic options.

No derivation, results, or comparison of strategies is provided; the text is a request for learning resources rather than a technical treatment. It establishes the basic setup and identifies important study questions, but does not specify a pricing model, rebalancing schedule, transaction costs, or market assumptions. Those details would be needed to assess practical hedging performance.

Key ideas

• A discrete delta hedge holds the underlying in proportion to the option’s delta.
• The bank account can balance trades so the hedging portfolio remains self-financing.
• Discrete rebalancing raises questions about convergence and hedge quality.
• The document seeks references on optimal strategies and hedging exotic options.

Tags

# Reference for delta hedging programmatically


# Reference for delta hedging programmatically












I learned some of the basic theory of Bjork (chap 1-9)

and would now like to study some (discrete delta) hedging using programming software.

We had an exercise in school where we hedged a call option by investing its delta in the underlying stock, and keeping the portfolio self-financing using the bank.

I thought this was very interesting, and liked the programming aspect of it, and would like to know if there is some reference that studies this a bit more professionally and rigorously, studying convergence issues, optimal hedging strategies, applications to more exotic options, etc.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.