# Questions tagged [stochastic-discount]

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### Average individual consumption growth vs average aggregate consumption growth

Consumption growth is an essential thing in most asset pricing models and usually the Euler equation defines the return of an asset as a covariance between consumption frowth and the cash-flows of ...
44 views

### Stochastic discount factor for factor research

Often, after presenting a new factor technique, the paper calculates an SDF by doing $\Sigma ^{-1}\mu_F$ i.e. mean variance optimization on the factors. What is the significance of doing this ?
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### The portfolio whose return is the stochastic discount factor

I am trying to construct a portfolio whose return is $a + bm_{t+1}$ where $a$ and $b$ are some constants for a certain investor. $m_{t+1}$ is the stochastic discount factor at time $t+1$. I am ...
501 views

### Real world monte-carlo (P-measure)

Consider the 2 following approaches to pricing a security: Monte-carlo ($\mathbb{Q}$-measure) $\begin{equation} C = \frac{1}{N} \sum_{i=1}^{n} e^{-rT} max(S_i(t) - K, 0) \end{equation}$ Monte-carlo ...
87 views

### Benchmarking option pricing under stochastic interest rates

I priced a long-term option (10 or 20 years) using two different models: one assumes constant interest rates, the other assumes stochastic interest rates. Is there a way (e.g. a benchmark) to ...
5k views

### Black-Scholes under stochastic interest rates

I'm trying to implement the Black-Scholes formula to price a call option under stochastic interest rates. Following the book of McLeish (2005), the formula is given by (assuming interest rates are ...
99 views

### How do I find the Sharpe Ratio?

Suppose I'm given two assets, $x_0$, $x_1$ and the stochastic discount factor m. How do I find $m_p$, then use it to compute Sharpe($R_p$)? Any help is greatly appreciated.
467 views

### Proving there exists no arbitrage opportunities given 3 states and 2 assets

Assume there are 3 states of the world: w1, w2, and w3. Assume there are two assets: a risk-free asset returning Rf in each state, and a risky asset with Return R1 in state w1, R2 in state w2, and R3 ...
398 views

### Data Selection for Empirical Pricing Kernel Estimation (Stochastic Discount Factor)

I want to estimate an empirical pricing kernel for an index. Hence, I need to estimate a physical and risk neutral density. For estimating the physical density, only the index data in an observed time ...
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### Discounting based on instrument type

Suppose we have an asset $A$, and we have modelled the cashflows for this asset to be $\{C_{1},\ldots C_{k}\}$ which occur at time $\{T_{1},\ldots T_{k}\}$. Now the present value of the asset can be ...