The Convergence Rate of Option Prices in Trinomial Trees
Abstract
:1. Introduction
2. -Nomial Models
3. The Main Theorem
4. Verification of the Result
4.1. Comparison with Chang and Palmer’s Binomial Model
4.2. Application of Theorem 1 to Trinomial Models
4.3. Numerical Results for the Trinomial Models
5. Proof of Theorem 1
6. Proof of Theorem 2
7. Proof of Theorem 3
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Appendix A
Appendix A.1. Properties of
- (i)
- , , and for , is a polynomial of degree at most ; in fact, for and ;
- (ii)
- the are bounded as functions of n.
Appendix A.2. On the Power Series of the Exponential of a Power Series
Appendix A.3. Properties of ψ
- (i)
- If for ,
- (ii)
- If is bounded and for , then for ,
- (iii)
- If is bounded and for , where α is real, then
- (iv)
- Suppose that
Appendix A.4. Replacing the Variance by the Sheppard-Corrected Variance in ψ
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Leduc, G.; Palmer, K. The Convergence Rate of Option Prices in Trinomial Trees. Risks 2023, 11, 52. https://doi.org/10.3390/risks11030052
Leduc G, Palmer K. The Convergence Rate of Option Prices in Trinomial Trees. Risks. 2023; 11(3):52. https://doi.org/10.3390/risks11030052
Chicago/Turabian StyleLeduc, Guillaume, and Kenneth Palmer. 2023. "The Convergence Rate of Option Prices in Trinomial Trees" Risks 11, no. 3: 52. https://doi.org/10.3390/risks11030052