The risk-neutral-measure tag has no wiki summary.
3
votes
2answers
196 views
Black-Scholes and Fundamentals
So basically
$dS_t=\mu S_tdt+\sigma S_tdWt$
and
$\mu=r-\frac12\sigma^2$
I have just been thinking about this later equation. This is very interesting because it ties together risk-free ...
4
votes
2answers
146 views
Is drift rate the same as interest rate in risk-neutral random walk when using Monte Carlo for option pricing?
When using following risk-neutral random walk
$$\delta S = rS \delta t + \sigma S \sqrt{\delta t} \phi$$
where $\phi \sim N(0,1)$.
Now when a text mentions drift = 5% does that mean that interest ...
2
votes
1answer
105 views
American Option price formula assuming a logLaplace distribution?
What are $d_1$ and $d_2$ for Laplace? may be running before walking.
When I tried to use the equations provided, the pricing became extremely lopsided, with the calls being routinely double puts. ...
6
votes
0answers
117 views
Consistency of economic scenarios in nested stochastics simulation
I am interested in references on research regarding the consistency of economic scenarios in nested stochastics for risk measurement.
Background:
Pricing by Monte-Carlo:
For pricing complex ...
2
votes
1answer
113 views
How to choose model parameters?
I'm studying math and attend this semester a course about interest rates. Now, some questions show up how exactly things are working in the real world.
My examples will be about interest rates ...
1
vote
1answer
87 views
Pricing forward contract on a stock
Please tell me where I've gone wrong (if I did in fact make a mistake). I'm pricing a long forward on a stock. The usual setup applies:
This has payoff $S(T) - K$ at time $T$.
We are at $t$ now.
...
1
vote
0answers
82 views
Pricing a Power Contract derivative security
I'm trying to price a "power contract" and would appreciate guidance on the next step. The payoff at time $T$ is $(S(T)/K)^\alpha$, where $K > 0$, $\alpha \in \mathbb{N}$, $T > 0$. $S$ is ...
2
votes
0answers
101 views
Measure change in a bond option problem
This is not a homework or assignment exercise.
I'm trying to evaluate $\displaystyle \ \ I := E_\beta \big[\frac{1}{\beta(T_0)} K \mathbf{1}_{\{B(T_0,T_1) > K\}}\big]$, where $\beta$ is the ...
5
votes
2answers
363 views
Version of Girsanov theorem with changing volatility
Is there a version of Girsanov theorem when the volatility is changing?
For example Girsanov theorem states that Radon Nikodym (RN) derivative for a stochastic equation is used to transform the ...
2
votes
1answer
173 views
Risk neutral probability in binomial short rate model assumed to be 0.5?
This should be a basic question but I have not been able to find a satisfying explanation. In the simplest binomial model, the risk neutral probability is computed using the up/down magnitude and the ...
6
votes
2answers
338 views
How to transform process to risk-neutral measure for Monte Carlo option pricing?
I am trying to price an option using the Monte Carlo method, and I have the price process simulations as an inputs. The underlying is a forward contract, so at all times the mean of the simulations is ...
8
votes
2answers
155 views
St Petersburg lottery pricing & short investing horizons
I am a statistician (no solid background in finance). Please forward me to a book \ chapter \ paper to resolve the following general question.
Suppose we have a stock with the following monthly return ...
1
vote
1answer
225 views
Risk Neutral Probability and invariant measure
Is a risk-neutral probability a special case of an invariant measure?
5
votes
2answers
590 views
How does one go from measure P to Q(risk-neutral) when modeling an asset paying dividends?
I am really having a terrible time applying Girsanov's theorem to go from the real-world measure $P$ to the risk-neutral measure $Q$. I want to determine the payoff of a derivative based an asset ...
3
votes
2answers
127 views
What mathematical characteristics are required from the asset price process in order to stay within the RNP framework?
I'm currently doing a course in derivatives pricing and I'm having some trouble wrapping my head around the sweet spot where theory meets reality in terms of Risk Neutral Pricing.
I know that the ...
2
votes
2answers
425 views
Financial Mathematics - Martingales example
Was hoping somebody could help me with the following question.
Prove that under the risk-neutral probability $\tilde{\mathsf P}$ the stock and the bank account have the same average rate of growth. ...
10
votes
5answers
1k views
Formal proof for risk-neutral pricing formula
As you know, the key equation of risk neutral pricing is the following:
$\exp^{-rt} S_t = E_Q[\exp^{-rT} S_T | \mathcal{F}_t]$
That is, discounted prices are Q-martingales.
It makes real-sense for ...
