# Questions tagged [real-world-measure]

The tag has no usage guidance.

25 questions
Filter by
Sorted by
Tagged with
1 vote
111 views

### 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 ...
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 ...
1 vote
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 ...
• 21
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 ...
• 147
175 views

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 ...
• 552
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 ...
• 552
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 ...
• 1,426
1 vote
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 ...
• 2,806
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\...
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 ...
• 383
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 ...
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 ...
• 552
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 $\mathbb{P}$?
• 515