The sheet entitled "Margrabe Calculator" uses a model developed by Dr. William Margrabe to price Expirationless Options (XP
The macro security level must be set to "Medium" or lower and you must select "Enable Macros" when opening this file.
All required inputs are contained within the highlighted cells within the calculator worksheet. 1. 2. 3. 4. 5. 6.
Select the current price of the underlying asset and enter in cell B6 labeled "Underlying (S)". Select the volatility of the underlying asset and enter in cell B7 labeled "Volatility" (must be greater than zero). Select the dividend yield of the underlying asset and enter in cell B8 labeled "Dividend" (must be greater than zero). Select the current risk-free rate and enter in cell B9 labeled "Interest Rate" (must be greater than zero). Enter the appropriate strike prices for the XPO put and XPO call (do not have to be identical) in cells C13 and F13, respectiv Enter the desired interval between strike prices in cells A22 and I22 for the intervals between the strike prices.
The outputs generated in the two tables are as follows:
The XPO put and call prices for different values of the underlying asset with the XPO strike price held constant; and The XPO put and call prices for different strike prices with the underlying asset price held constant.
The charts below the two tables contain the following information:
The XPO put and call prices graphed simultaneously for a given strike price ("XPO Prices Given X"); The "time" value contained in the XPO put and call prices for a given strike price ("Time Values Given X"); The XPO put and call prices graphed simultaneously for a given underlying asset value ("XPO Prices Given S"); and The "time" value contained in the XPO put and call prices for a given underlying asset value ("Time Values Given S
e to price Expirationless Options (XPOs).
ros" when opening this file.
ator worksheet.
be greater than zero). (must be greater than zero). eater than zero). ntical) in cells C13 and F13, respectively. ween the strike prices.
e XPO strike price held constant; and price held constant.
XPO Prices Given X"); e ("Time Values Given X"); et value ("XPO Prices Given S"); and g asset value ("Time Values Given S").
Expirationless Option (XPO) Calculator (Graphs Below) Generalized Merton Method as Developed by Dr. William Margrabe
INPUTS
Underlying (S) Volatility Dividend Interest Rate Strike (X) (shaded) XPO Put $ 30.00 20% 1.68% 3.00% $ 25.00 Delta #NAME? Put TV #NAME? $ 25.00 XPO Call Price Delta ####### Call TV #NAME? XPO Call
OUTPUTS
XPO Put Price
#NAME?
#NAME?
XPO Prices for DIFFERENT UNDERLYING Prices, Given X Above
X= Interval 5 $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $
XPO Put $ 25.00
XPO Put Delta #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME?
X= Put TV #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME?
XPO Call $ 25.00
XPO Call Delta ####### ####### ####### ####### ####### ####### ####### ####### ####### ####### ####### ####### ####### ####### ####### ####### ####### ####### ####### ####### ####### ####### ####### ####### ####### ####### ####### ####### ####### Call TV 0.00 #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME?
S
5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140 145
#NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME?
$
#NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME?
$ $ $ $ $ $ $ $ $ $
150 155 160 165 170 175 180 185 190 195
#NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME?
#NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME?
#NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME?
#NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME?
####### ####### ####### ####### ####### ####### ####### ####### ####### #######
#NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME?
Vol.= 20%
Div.=
1.68%
Int. Rate=
3.00%
XPO Prices Given X
$120 $100 XPO Price
$80 $60 $40 $20 $0
$$25 $50 $75 $100 $125 $150 $175
Asset Price
Put Price Call Price
Vol.=
20%
Div.=
1.68% Int. Rate=
3.00%
Time Values Given X
$100 $80
XPO Time Value
$60 $40
$20
$0
$$25 $50 $75 $100 $125 $150 $175
Asset Price
TV Put TV Call
XPO Prices for DIFFERENT STRIKE Prices, Given S Above
S= Interval 5 $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $
XPO Put $ 30.00
XPO Put Delta 0 #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? Put TV 0.00 ###### ###### ###### ###### ###### ###### ###### ###### ###### ###### ###### ###### ###### ###### ###### ###### ###### ###### ###### ###### ###### ###### ###### ###### ###### ###### ###### ###### ######
S=
XPO Call $ 30.00
XPO Call Delta 100 ####### ####### ####### ####### ####### ####### ####### ####### ####### ####### ####### ####### ####### ####### ####### ####### ####### ####### ####### ####### ####### ####### ####### ####### ####### ####### ####### ####### ####### Call TV 0.00 #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME?
X
5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140 145
$
#NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME?
$
30.00 #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME?
$ $ $ $ $ $ $ $ $ $
150 155 160 165 170 175 180 185 190 195
#NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME?
#NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME?
###### ###### ###### ###### ###### ###### ###### ###### ###### ######
#NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME?
####### ####### ####### ####### ####### ####### ####### ####### ####### #######
#NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME?
Vol.=
20%
Div.=
1.68%
Int. Rate=
3.00%
XPO Prices Given S
$35 $30 XPO Price $25
$20
$15 $10 $5 $0 $0 $25 $50 $75 $100 $125 $150 $175 Strike Price
Call Price Put Price
Vol.=
20%
Div.=
1.68%
Int. Rate=
3.00%
Time Values Given S
$100 XPO Time Value $80 $60
$40
$20 $0
$$25 $50 $75 $100 $125 $150 $175
Strike Price
TV Put TV Call
William Margrabe, Ph.D., President The William Margrabe Group, Inc.
Academic Career 1970-1985, 1995 - present William Margrabe began his foundation in analytics at the Johns Hopkins University, where he earned his B.A. in economics (Phi Beta Kappa) in 1970. At the University of Chicago, he began learning about financial models in 1971 when Gene Fama introduced him to Markowitz portfolio theory. In 1973, William Margrabe worked as Fischer Black’s research and teaching assistant. The University of Chicago awarded William Margrabe his Ph.D. in economics in 1978. Professor Margrabe taught finance at: University of Illinois at Chicago Circle, 1972-1974 Wharton School of Business, 1975-1978 University of Pittsburgh, 1978-1981 George Washington University, 1981-1985 New York University, 1995-1997 Experience with Derivatives on "Wall Street" and MBS, 1985-1994 After earning tenure, professor Margrabe spent his sabbatical leave as consultant and senior economist for Freddie Mac (1985-1987). Dr. Margrabe then worked on Wall Street for about seven years at: Salomon Brothers, 1993-1994 Morgan Stanley, 1991-1993 Bankers Trust, 1987-1991 Risk Management and Derivatives Consulting since 1994 Dr. Margrabe founded the William Margrabe Group, Inc. in 1994 to meet the obvious supply side analytical needs, but found even stronger demand on the sell side. Since that time, the Margrabe Group has delivered knowledge and software for risk management and derivatives pricing to buy side, sell side and regulators. Its core business lines include: Reviewing and documenting proprietary and third-party software for pricing and risk management (market makers, life insurance companies, risk managers, internal auditors, controllers) Advising on operational risk of derivatives models (risk managers, internal auditors, controllers, directors) Building prototype risk management software (risk arbitrage department of investment bank) Building advanced pricing models (derivatives dealers risk management (derivatives dealers, Federal Reserve Presenting the mathematics of derivatives pricing and and market makers, insurance company) Board, ICM and Risk magazine courses (NYU, GWU) Presenting the elements of derivatives (Derivatives Boot Camp) The Margrabe Group’s list of clients includes: American Stock Exchange Banque Paribas Chase Bank Fannie Mae Federal Reserve Board Morgan Stanley Selected Publications As "Dr. Risk", William Margrabe regularly communicates what he has learned via the monthly column, "Ask Dr. Risk", available on the Internet in The Derivatives ‘Zine (http://www.margrabe.com) and frequently in Derivatives Strategy . Other selected publications include: "Selecting and Customizing Equity Derivatives for Investment Funds." In Equity Derivatives; Applications in Risk Management and Investment . London: Risk Publications, 1997. "Triangular Option Arbitrage." Journal of Derivatives (1994). "The Value of an Option to Exchange One Asset for Another." Journal of Finance (1978).
Disclaimer: The Margrabe XPO option calculator is being provided for general educational and informational only and should not be considered complete, precise, or current. The calculator has been provided to assist interested parties in learning how theoretical XPO option prices and risk parameters are calculated. The XPO calculator is not to be used as the basis for any investment or risk management decisions and only represents one theoretical approach for pricing expirationless options.