# Tag Info

0

There was a post in QF a while ago suggesting at least 5000 data points (in the time series) for a GARCH model

1

Any of a wide variety of local vol models, where (from your equation) $b(\cdot,\cdot)$ is some fitted surface, are unlikely to have closed-form solutions for the terminal distribution. Indeed it's well-known that these models tend to have very unusual forward term structures of volatility. As a specific example, take $b(\cdot,\cdot)$ to be an approximation ...

1

I would answer your question with no. First: what do you need the risk free rate for? If you want to price equity derivatives then probably a short money market rate would better fit this purpose. Second: the maturity. Look at yield curves. The short end is usually at very different level than the 10 year rate. So two times no. A small "no" for taking ...

3

If you allow $X_t$ to be two dimensional then a model with a stock price $X_t^1$ and its variance process $X_t^2$ (stochastic volatility) would fit your definition. In such cases to my knowledge we often don't have a closed form of the density of $X_T^1$ but in some cases we have a closed form of the Laplace transform. An example is the Heston model.

0

You can try KineTick, free EndOfDay data http://www.kinetick.com/end-of-day

1

It's been quite a while since I did this stuff, but I'll add my input. Please correct me if appropriate. $\{H < T\} = \{ \sup_{0\leq s \leq T} (S_{0} + \sigma B_{s}) > a \} = \{\sup_{0 \leq s \leq T} B_s > \frac{a-S_0}{\sigma}\}$. Set $\mu := \frac{a-S_0}{\sigma}$ and $M_{T} := \sup_{0 \leq s \leq T} B_{s}$. Then, \$P(\{H < T\} = P(\{M_T > ...

3

The general idea is to bootstrap the discount factors in the correct order, based on the data you have given. I'm going to make some assumptions that your bonds are paying annual coupons. The longest maturity is 2.5 years, meaning you need discount factors for 6M, 1.5Y and 2.5Y. The 6M deposit has a rate of 5%, this tells you that you should use the 5% rate ...

2

The essence of discounting is that now is less risky than later. So a contract to deliver £1 in 1 year is more risky than one to deliver £1 tomorrow, (the counterparty could suffer a credit event) so it is worth less. Discount factors multiply; if I know that £1 at 1y is worth £0.98 today, and £1 at 2y is worth £0.98 at 1y (i.e. equal rates for both ...

Top 50 recent answers are included