FINA 6750 Urgent
Black-Scholes-Merton & Binomial
| Inputs: | Black-Scholes-Merton Model | Binomial Model | |||||
| Asset price (S0) | 699.49 | European | European | Steps: | 100 | ||
| Exercise price (X) | 695 | Call | Put | European | European | ||
| Time to expiration (T) | 0.1288 | Price | 18.8015 | 9.9471 | Call | Put | |
| Standard deviation (s) | 14.00% | Delta (D) | 0.6098 | -0.3902 | Price | 13.5523 | 12.0788 |
| Risk-free rate (r or rc) | 4.89% | Gamma (G) | 0.0109 | 0.0109 | Delta (D) | 0.5700 | -0.4300 |
| Dividends: | 0.00% | Theta (Q) | -72.3091 | -38.5218 | Gamma (G) | 0.0121 | 0.0121 |
| continuous yield (dc) or discrete dividends below: | Vega | 96.3225 | 96.3225 | Theta (Q) | -68.9155 | -63.3643 | |
| Rho | 52.5009 | -36.4301 | American Call | American | |||
| Call | Put | ||||||
| d1 | 0.2787 | Price | 13.5523 | 12.1121 | |||
| d2 | 0.2285 | Delta (D) | 0.5700 | -0.4316 | |||
| N(d1) | 0.6098 | Gamma (G) | 0.0121 | 0.0121 | |||
| N(d2) | 0.5904 | Theta (Q) | -68.9155 | -63.7694 | |||
| PV of divs | 0.0000 | ||||||
| PV of strike | 690.6356 | ||||||
| Dividend # | Dividend | Time to ex date | Present Value | S – PV divs | 699.4900 | ||
| 1 | 0.0000 | ||||||
| 2 | 0.0000 | ||||||
| 3 | 0.0000 | ||||||
| 4 | 0.0000 | ||||||
| 5 | 0.0000 | ||||||
| 6 | 0.0000 | ||||||
| 7 | 0.0000 | ||||||
| 8 | 0.0000 | ||||||
| 9 | 0.0000 | ||||||
| 10 | 0.0000 | ||||||
| 11 | 0.0000 | ||||||
| 12 | 0.0000 | ||||||
| 13 | 0.0000 | ||||||
| 14 | 0.0000 | ||||||
| 15 | 0.0000 | ||||||
| 16 | 0.0000 | ||||||
| 17 | 0.0000 | ||||||
| 18 | 0.0000 | ||||||
| 19 | 0.0000 | ||||||
| 20 | 0.0000 | ||||||
| 21 | 0.0000 | ||||||
| 22 | 0.0000 | ||||||
| 23 | 0.0000 | ||||||
| 24 | 0.0000 | ||||||
| 25 | 0.0000 | ||||||
| 26 | 0.0000 | ||||||
| 27 | 0.0000 | ||||||
| 28 | 0.0000 | ||||||
| 29 | 0.0000 | ||||||
| 30 | 0.0000 | ||||||
| 31 | 0.0000 | ||||||
| 32 | 0.0000 | ||||||
| 33 | 0.0000 | ||||||
| 34 | 0.0000 | ||||||
| 35 | 0.0000 | ||||||
| 36 | 0.0000 | ||||||
| 37 | 0.0000 | ||||||
| 38 | 0.0000 | ||||||
| 39 | 0.0000 | ||||||
| 40 | 0.0000 | ||||||
| 41 | 0.0000 | ||||||
| 42 | 0.0000 | ||||||
| 43 | 0.0000 | ||||||
| 44 | 0.0000 | ||||||
| 45 | 0.0000 | ||||||
| 46 | 0.0000 | ||||||
| 47 | 0.0000 | ||||||
| 48 | 0.0000 | ||||||
| 49 | 0.0000 | ||||||
| 50 | 0.0000 | ||||||
| 51 | 0.0000 | ||||||
| 52 | 0.0000 | ||||||
| 53 | 0.0000 | ||||||
| 54 | 0.0000 | ||||||
| 55 | 0.0000 | ||||||
| 56 | 0.0000 | ||||||
| 57 | 0.0000 | ||||||
| 58 | 0.0000 | ||||||
| 59 | 0.0000 | ||||||
| 60 | 0.0000 | ||||||
| 61 | 0.0000 | ||||||
| 62 | 0.0000 | ||||||
| 63 | 0.0000 | ||||||
| 64 | 0.0000 | ||||||
| 65 | 0.0000 | ||||||
| 66 | 0.0000 | ||||||
| 67 | 0.0000 | ||||||
| 68 | 0.0000 | ||||||
| 69 | 0.0000 | ||||||
| 70 | 0.0000 | ||||||
| 71 | 0.0000 | ||||||
| 72 | 0.0000 | ||||||
| 73 | 0.0000 | ||||||
| 74 | 0.0000 | ||||||
| 75 | 0.0000 | ||||||
| 76 | 0.0000 | ||||||
| 77 | 0.0000 | ||||||
| 78 | 0.0000 | ||||||
| 79 | 0.0000 | ||||||
| 80 | 0.0000 | ||||||
| 81 | 0.0000 | ||||||
| 82 | 0.0000 | ||||||
| 83 | 0.0000 | ||||||
| 84 | 0.0000 | ||||||
| 85 | 0.0000 | ||||||
| 86 | 0.0000 | ||||||
| 87 | 0.0000 | ||||||
| 88 | 0.0000 | ||||||
| 89 | 0.0000 | ||||||
| 90 | 0.0000 | ||||||
| 91 | 0.0000 | ||||||
| 92 | 0.0000 | ||||||
| 93 | 0.0000 | ||||||
| 94 | 0.0000 | ||||||
| 95 | 0.0000 | ||||||
| 96 | 0.0000 | ||||||
| 97 | 0.0000 | ||||||
| 98 | 0.0000 | ||||||
| 99 | 0.0000 | ||||||
| 100 | 0.0000 | ||||||
| = | = | = | = | ||||
| Sum | 0.0000 | ||||||
| Do not change the items below****************************** | |||||||
| discrete | 2 | continuous risk-free rate | |||||
| continuous |
BLACK-SCHOLES & BINOMIAL OPTION PRICING MODELS bsbin3.xls
In lieu of a continuously compounded yield, place below up to one hundred discrete dividends and the time in years to each ex-dividend date. Leave all unused cells blank. Set the yield above to zero. If yield is not set to zero, all discrete dividends are disregarded.
Black-Scholes-Merton and Binomial Option Pricing 10e
Run Binomial Model
Instructions
Instructions: Insert values in highlighted cells. Risk-free rate, standard deviation and yield can be entered as decimal or percentage (e.g., .052 or 5.2 for 5.2 %). Select form (discrete or continuous) for risk-free rate. Black-Scholes values automatically recalculate. Click on “Run Binomial Option Pricing Model” button to recalculate binomial values. Input cells have double borders. Output cells have single borders. Up to 5,000 time steps can be used in the binomial model. Input a continuous dividend yield or up to 0 discrete dividends. Do not enter both or the discrete dividends will be ignored. This spreadsheet can be used to calculate options on forwards or futures using the Black variation of the Black-Scholes model. Input the forward or futures price instead of the asset price and input the risk-free rate as both the risk-free rate and the dividend yield. Do not enter discrete dividends. To price foreign currency options, input the spot rate as the asset price, the domestic interest rate as the risk-free rate and the foreign interest rate as the dividend yield. Do not enter discrete dividends.
About
Written by Don M. Chance and Robert Brooks For use with An Introduction to Derivatives and Risk Management, 10th ed. (Mason, Ohio: Cengage, 2015) Date: 7/09 Last updated: 3/18/14 Ā© 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
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