This thesis focuses on binomial tree approximation for solving Backward Stochastic Differential Equations (BSDEs), particularly in the context of option pricing. The numerical method iteratively solves the discrete-time version of the BSDE backward in time. The discretization process employs constructing a binomial tree representing possible future price movements of the underlying asset. At each node of the tree, the option value is computed based on the expected payoff at that node and the discounted option values from the subsequent nodes. Furthermore, we discusses an approximation for the control process Z,, and the replicating portfolio a,. Which is expressed as the conditional expectation of the ratio of future option value increment to Brownian motion increment and demonstrate how it relates to the Black Scholes model for continuous time. An important part of the thesis is to compare theoretical expressions from the Black-Scholes model and the binomial tree. Formulas from the binomial tree are explicitly calculated and validated by numerical experiments.
| Identifer | oai:union.ndltd.org:UPSALLA1/oai:DiVA.org:lnu-130416 |
| Date | January 2024 |
| Creators | Ummulbanin, Ummulbanin |
| Publisher | Linnéuniversitetet, Institutionen för matematik (MA) |
| Source Sets | DiVA Archive at Upsalla University |
| Language | English |
| Detected Language | English |
| Type | Student thesis, info:eu-repo/semantics/bachelorThesis, text |
| Format | application/pdf |
| Rights | info:eu-repo/semantics/openAccess |
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