discount factor

• Discount factor

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Patent valuation - Income-based method

1 This method is based on the principle that the value of an asset is intrinsic to the

expected income flows it generates. After the income is estimated, the result is

discounted by an appropriate discount factor with the objective to adjust it to the

present circumstances and therefore to determine the net present value of the intellectual property. There are different methods of calculation of the future cash

flows, such as: https://store.theartofservice.com/the-discount-factor-toolkit.html

Patent valuation - Income-based method

1 # Discounted cash flow method: This method aims to estimate future cash flows, which are projected and after

discounted by applying an appropriate discount factor. The main source of information to estimate the cash flows is generally the business plan of the company that exploits or

intends to exploit the asset.


Patent valuation - Toolip Valuation

1 It also manages information about legal data (patent validity, extension

countries, remaining term) and financial data (annual turnover,

expected growth in the company or market, discount factors), and also covering technological, strategic or marketing aspects of the patented

technology


Stern Review on the Economics of Climate Change - Inherent discounting

1 He supports the discount factors used in the Stern analysis,

particularly the view that discounting should reflect only the probability that the world will end at a given

future date, and not the impatience of an infinitely lived representative

consumer.)


Hyperbolic discounting - Formal model

1 where f(D) is the discount factor that multiplies the value of the reward, D is the delay in the reward, and k is a parameter governing the degree of discounting. This is compared with

the formula for exponential discounting:


Hyperbolic discounting - Quasi-hyperbolic approximation

1 where β and δ are constants between 0 and 1; and again D is the delay in the reward, and f(D) is the discount

factor. The condition f(0) = 1 is stating that rewards taken at the present time are not discounted.


Stock valuation - Limited high-growth period approximation

1 and hence are extremely sensitive to the difference of dividend growth to

discount factor. One might argue that an analyst can justify any value (and

that


Model (economics) - Omitted details

1 * In turn, environmental economics has been accused of omitting key financial considerations from its

models. For example the returns to solar power investments are

sometimes modelled without a discount factor, so that the present utility of solar energy delivered in a century's time is precisely equal to

gas-power station energy today.https://store.theartofservice.com/the-discount-factor-toolkit.html

At the money - Simple examples

1 Note that once logs are taken, moneyness in terms of forward or

spot differ by an additive factor (log of discount factor), as \ln\left(F/K\

right) = \ln(S/K)+rT.


Discounting - Discount factor

1 The 'discount factor', DF(T), is the factor by which a future cash flow

must be multiplied in order to obtain the present value. For a zero-rate

(also called spot rate) r, taken from a yield curve, and a time to cashflow T

(in years), the discount factor is:



1 In the case where the only discount rate you have is not a zero-rate (neither taken from a zero-coupon bond nor converted from a swap rate to a zero-rate through

Bootstrapping (finance)|bootstrapping) but an annually-compounded rate (for example

if your benchmark is a US Treasury bond with annual coupons and you only have its

yield to maturity, you would use an annually-compounded discount factor:



1 In that case, the discount factor is then (if the usual money market day count convention for the currency is ACT/360, in case of currencies such as USD, EUR, JPY), with r the zero-rate and T the time to cashflow in

years:


Welfare cost of business cycles - Mathematical representation and formula

1 Lucas sets up an infinitely lived representative agent model where

total lifetime utility(U is given by the present discounted value (with \beta

representing the Discount factor#Discount factor|discount

factor) of per period utilities (u(.)) which in turn depend on

consumption in each period (c_t)


Valuation using multiples - Determining discount rate / factor

1 VirusControl has chosen their discount rate very high as their

company is potentially very profitable but also very risky. They

calculate their discount factor based on five years.


Valuation using multiples - Determining current company value

1 Calculate the current value of the future company value by multiplying

the future business value with the discount factor. This is known as the

time value of money.


Valuation using multiples - Determining current company value

1 VirusControl multiplies their future company value with the

discount factor:https://store.theartofservice.com/the-discount-factor-toolkit.html

Impulsive behaviour - Intertemporal choice

1 Many studies suggest that humans and animals discount future values

according to a hyperbolic discounting curve where the discount factor decreases with the length of the delay (for example, waiting from

today to tomorrow involves more loss of value than waiting from twenty

days to twenty-one days)


Price leadership - Duopoly example

1 To be more precise, suppose that firms have a Discounting#Discount factor|discount factor \delta. The discounted value of the cost to cheating and being punished

indefinitely are


Inverted yield curve - Market expectations (pure expectations) hypothesis

1 The significant difficulty in defining a yield curve therefore is to determine

the function P(t). P is called the discount factor function.


Inverted yield curve - Market expectations (pure expectations) hypothesis

1 Let the vector F represent today's prices of the instrument (so that the i-th instrument has value F(i)), then by definition of our discount factor function P we should have that F = AP (this is a matrix multiplication)


Impulsivity - Intertemporal choice

1 Many studies suggest that humans and animals discount future values

according to a hyperbolic discounting curve where the discount factor decreases with the length of the delay (for example, waiting from

today to tomorrow involves more loss of value than waiting from twenty

days to twenty-one days)


Risk-neutral measure - Usage

1 Risk-neutral measures make it easy to express the value of a derivative in a formula. Suppose at a future time T a

derivative (e.g., a call option on a stock) pays H_T units, where H_T is a random

variable on the probability space describing the market. Further suppose that the discount factor from now (time zero) until time T is P(0, T). Then today's

fair value of the derivative is


Folk theorem (game theory)

1 The folk theorem states that any feasible payoff profile that strictly

dominates the minmax profile can be realized as a Nash equilibrium payoff

profile, with sufficiently large discount factor.


Folk theorem (game theory) - Sketch of proof

1 In more detail, assume that the payoff of a player in an infinitely repeated game is given by the

average discounted criterion with discount factor 0 δtt \geq 011-\

delta \epsilon.


Stochastic discount factor

1 A 'Stochastic discount factor (SDF)' is a concept in financial economics and

mathematical finance.


Stochastic discount factor

1 This definition is of fundamental importance in Valuation (finance)|asset pricing. The name stochastic

discount factor reflects the fact that the price of an asset can be

computed by discounting the future cash flow \tilde_i by the stochastic factor \tilde and then taking the

expectation.


Stochastic discount factor - Other names

1 The stochastic discount factor is sometimes referred to as the 'pricing kernel'. This name comes from the

fact that if the expectation


Integral kernel - Motivation

1 Also there are many applications of probability that rely on integral

transforms, such as pricing kernel or stochastic discount factor, or the smoothing of data recovered from

robust statistics, see kernel (statistics).


Kernel - Finance

1 * Pricing kernel, another name for the stochastic discount factor used in asset

pricing


Greeks (finance) - Practical use

1 By put–call parity, long a call and short a put equals a forward F, which is linear in the spot S, with factor the inverse of the discount factor, so the

derivative dF/dS is this factor.


Greeks (finance) - Practical use

1 50 Delta put and 50 Delta call are not quite identical, due to spot and forward differing by the discount

factor, but they are often conflated.


Monte Carlo methods in finance - Mathematically

1 where _T is the discount factor corresponding to the risk-free rate to the final maturity date T years into

the future.


Put-call parity - Statement

1 The assets C and P on the left side are given in current values, while the

assets F and K are given in future values (forward price of asset, and

strike price paid at expiry), which the discount factor D converts to present

values.


Bond convexity - How bond duration changes with a changing interest rate

1 As the interest rate increases, the present value of longer-dated

payments declines in relation to earlier coupons (by the discount factor between the early and late

payments)


Annual effective discount rate

1 It is the annual discount factor to be applied to the future cash flow, to

find the discount, subtracted from a future value to find the value one

year earlier.


Discounted - Discount factor

1 In that case, the discount factor is then (if the usual money market day count convention for the currency is ACT/360, in case of currencies such

as United States dollar, euro, Japanese yen), with r the zero-rate

and T the time to cash flow in years:


Best places in the US to retire

1 Ranking methodologies have a mixture of Subjectivity|subjective

and statistical elements, and some surveys discount factors such as

Climate, while others emphasize it


Bootstrapping (finance)

1 #Derive discount factors for all terms, these are the internal rates of return of the bonds


Bellman equation - A dynamic decision problem

1 Finally, we assume impatience, represented by a discount factor 0 \

betaPrinciple of Optimality: An optimal policy has the property that whatever the initial state and initial

decision are, the remaining decisions must constitute an optimal policy with regard to the state resulting

from the first decision


Gretna, Dumfries and Galloway - Present day

1 Much of the local economy is driven by the Marriage in Scotland|marriage industry,

where by some accounts, as many as one of every six Scottish weddings takes place in

Gretna / Gretna Green. Most marriages take place in Gretna itself, at the Register office, the Anvil Hall, or in the numerous Hotels in

the centre of the township. Gretna is also the location of the Gretna Gateway Outlet

Village, a development of discount factory shops.


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