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Questions tagged [real-world-measure]

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Analytical formula for discounted exposure of a European Put on a stock in Real-World measure

Is there an analytical formula to approximate the discounted exposure for a European Put on a Stock in the Real-World measure? This is just an initial phase to be able to assess the accuracy of using ...
Rhoyourway's user avatar
2 votes
0 answers
104 views

Largest class of real world probability models admitting explicit risk-neutral change of measure

Assume we have two assets, a random asset $A_t$ and deterministic risk-free bond $B_t = e^{rt}$. Let $P$ be a model of the real-world probabilities of $S$ and $Q$ the unique associated risk-neutral ...
quant3333's user avatar
1 vote
0 answers
104 views

How to get Risk-Neutral Drift for Trading Volume from Time Series

I am trying to price an option with Monte-Carlo simulation, where the payoff depends on some constants and a time-series (trading volume) which I model to follow a GBM. Now if I understood it ...
Merwin's user avatar
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2 votes
1 answer
711 views

Real world probabilities from option implied risk neutral density?

The work of Breeden and Litzenberger-formula (https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2642349) gives us a risk neutral probability distribution of a stock price, depending on the option ...
Lejoon's user avatar
  • 147
0 votes
0 answers
175 views

Real Option Valuation using simulation: real world vs risk neutral measure

I am trying to value a real option in the form of a software investment using a simulation. The software investment yields to daily revenues $R_t$ and costs $C_t$. Here are the formulas for these: $$...
Arely's user avatar
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1 vote
0 answers
257 views

Value at risk, risk-neutral vs real-world probability measures

Does anyone know if there is any link between the Value at Risk of risk-neutral distribution and of the real-world distributions of asset rate of returns?
Almostsurely's user avatar
1 vote
1 answer
367 views

Objective probability of default from CDS spread

I have the risk neutral probability of default extrapolated from the market data of the CDS spreads. How can I empirically estimate the market risk price of the objective probability of default (i.e. ...
d0whes's user avatar
  • 47
2 votes
1 answer
204 views

Variance-Covariance Matrix under $\mathbb{P}$ and $\mathbb{Q}$

I'd like to understand why $\Sigma$ is the same under both measures $\mathbb{P}$ and $\mathbb{Q}$. Is it an assumption or a general fact based on theoretical concepts?
morgan's user avatar
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2 votes
0 answers
34 views

Does equity premium puzzle affect option-implied RWDs using Arrow-Debreu equilibrium?

I am researching and learning about option-implied RNDs (risk neutral densities) and transformation to RWDs (risk world densities) using expected utility theory to compute risk aversion values. This ...
br0323's user avatar
  • 61
2 votes
2 answers
210 views

Heath–Jarrow–Morton under real-world measure

In HJM model (framework), the drift of the forward is determined by its diffusion coefficient: $$ \mu(t,s) = \sigma(t,s)\int_t^s \sigma(t,v)^Tdv $$ My understanding, is that the change of measure ...
Confounded's user avatar
3 votes
2 answers
101 views

Estimating risk aversion from option bid-ask spreads

Is it possible to use bid-ask spreads on contracts from a specific tenor to estimate risk aversion and use it to transform risk-neutral density into real-world density?
sle's user avatar
  • 121
4 votes
1 answer
487 views

Are all change of measure operations between equivalent probability measures Doléans-Dade exponentials?

Let $(\Omega, \mathcal{F}, \mathbb{F}, \mathbb{P})$ be a filtered probability space, where $\mathbb{F}=\left(\mathcal{F}\right)_{t\in[0;T]}$ and $\mathcal{F}=\mathcal{F}_T$. Let $(W_t)_{t\in[0;T]}$ be ...
fwd_T's user avatar
  • 747
2 votes
0 answers
273 views

Stochastic Volatility Models Real World Calibration

I am trying to find some research pertaining to the historical (or real world) calibration of stochastic volatility models. For example, in applications such as counterparty credit risk (IMM) or ...
VLT's user avatar
  • 81
3 votes
2 answers
2k views

Risk Neutral and Real World Valuations using Monte Carlo

Assume I'm an investor that wants to sell exotic put options. No one else is selling my kind of put option, so I need to determine my own "Market Price" through Monte Carlo simulation. I know that by ...
Mild_Thornberry's user avatar
2 votes
0 answers
160 views

State price deflator in the Vasicek model

I am trying to implement a simple bond pricing model using state price deflators in a Vasicek model. I am simulating paths of the processes $$\mathrm{d}r^{P} =\kappa^{P}(\theta^P - r^P(t))\mathrm{d}t ...
Martin Steen Andersen's user avatar
4 votes
3 answers
817 views

Are all changes of measures for continuous diffusion processes given by the change of drift?

In elementary discussions on change of measure for geometric Brownian motion, one often find statements like "change of measure = change of drift". Given a general continuous diffusion process of the ...
Confounded's user avatar
6 votes
1 answer
599 views

Estimation of Radon–Nikodym derivative from historical returns and option price data

Say we have an estimate of empirical density function $f^{\mathbb{P}}_S(s)$ of historical log-returns on a stock $S$ over a 30-day period under the real-world objective measure $\mathbb{P}$. We also ...
Confounded's user avatar
4 votes
1 answer
764 views

Uniqueness of Risk-neutral measure: Probabilistic view

Suppose we are working on the Black and Scholes Framework. There are only two assets, the risk-less bank account and a stock. The discounted process is a GBM under the physical measure with drift term ...
alexbougias's user avatar
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1 vote
1 answer
1k views

Confusion regarding the risk neutral and physical measures

I may be confused. I am looking at the risk neutral vs. physical measures. We know that knowing the short interest rate stochastic process $r$, a bond maturing at time $T$ can be considered as a ...
Hans's user avatar
  • 2,806
4 votes
1 answer
2k views

Vasicek short rate: Risk-neutral measure into real-world measure

I consider the Vasicek model under the risk-neutral measure $\mathbb{Q}$: $$ dr_t=\kappa(\theta−r_t) dt+\sigma dW^{\mathbb{Q}}_t.$$ I have already determined $$\mathbb{E}^{\mathbb{Q}}\left[e^{−\int\...
Stephanie's user avatar
3 votes
0 answers
131 views

Equivalent martingale measure in time changed Levy models

I am investigating time changed Levy models. As far as I have seen, these models are usually directly described under the risk neutral measure $\mathbb{Q}$. However, I'm interested in first modelling ...
lbf_1994's user avatar
  • 383
0 votes
2 answers
386 views

Stock forward price argument

Hi I am strangling to understand where is the mistake with the following strategy. Can anyone help me with the following argument? Assuming a stock price follows geometric Brownian motion then the ...
Unknown's user avatar
3 votes
0 answers
115 views

Change of measure when calibrating real-world dynamics

If I want to simulate a process (say, a set of forward rates) under a real-world measure, can I use option prices / implied vols to calibrate some of the parameters and do I need to change the measure ...
Confounded's user avatar
9 votes
2 answers
1k views

What is the numeraire for the real world measure $\mathbb{P}$?

We know the numeraires for the forward measure, the risk-neutral measure, etc. What is the numeraire for the real world measure $\mathbb{P}$?
user1559897's user avatar
38 votes
6 answers
14k views

How to estimate real-world probabilities

In the world of finance, Risk-neutral pricing allow us to estimate the fair value of derivatives using the risk free rate as the expected return of the underlyings. However, the behavior of ...
sets's user avatar
  • 1,471