The Black-Scholes-Merton dual equation
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2019
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866914800242524160 |
|---|---|
| author | Guo, Shuxin Liu, Qiang |
| author_facet | Guo, Shuxin Liu, Qiang |
| contents | We derive the Black-Scholes-Merton dual equation, which has exactly the same form as the Black-Scholes-Merton equation. The novel and general equation works for options with a payoff of homogeneous of degree one, including European, American, Bermudan, Asian, barrier, lookback, etc., and leads to new insights into pricing and hedging. Perceptibly, a put-call equality emerges - all the put options can be priced as their corresponding calls by simultaneously swapping stock price (dividend yield) for strike price (risk-free rate), and vice versa. Equally important, we provide simple analytic formulas for hedging parameters delta and gamma, which elevate the put-call equality to true practical applicability. For futures options, the put-call equality leads to "symmetric" properties between puts and calls or among puts (calls). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1912_10380 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | The Black-Scholes-Merton dual equation Guo, Shuxin Liu, Qiang Pricing of Securities Mathematical Finance Risk Management 91G20 We derive the Black-Scholes-Merton dual equation, which has exactly the same form as the Black-Scholes-Merton equation. The novel and general equation works for options with a payoff of homogeneous of degree one, including European, American, Bermudan, Asian, barrier, lookback, etc., and leads to new insights into pricing and hedging. Perceptibly, a put-call equality emerges - all the put options can be priced as their corresponding calls by simultaneously swapping stock price (dividend yield) for strike price (risk-free rate), and vice versa. Equally important, we provide simple analytic formulas for hedging parameters delta and gamma, which elevate the put-call equality to true practical applicability. For futures options, the put-call equality leads to "symmetric" properties between puts and calls or among puts (calls). |
| title | The Black-Scholes-Merton dual equation |
| topic | Pricing of Securities Mathematical Finance Risk Management 91G20 |
| url | https://arxiv.org/abs/1912.10380 |