# Tag Info

Accepted

### Figure of Stopping and Continuation Region

The exercise boundary $B_t$ for a finite maturity American put option is not a constant function of time as in your plot. As mentioned in the excerpt, $B_T = K$ at maturity. But for $t < T$, we ...
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### Which references would be useful as an introduction to econometrics as it pertains to CONTINUOUS TIME models?

This is seen as a bit of a niche field, which is likely why there are not so many books and these issues are not covered in standard econometrics texts. Options pricing models are usually fitted to ...
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### Black Scholes in Practice: Delta Hedging

1.) in textbooks usually stochastic differential $d$ is used which is rigourous 2.) delta heding in Black Scholes worldis perfect as it's the only way to eliminate risk completely in non friction ...
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### Why can't/doesn't the Fed adjust the federal funds interest rate continuously?

The Fed (under the Yellen regime) has always stated that any adjustments to the Federal Funds rate are "data dependent." These data points (CPI inflation, inflation expectations, non-farm payrolls, ...
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### Pricing Secured Barrier Call

The goal of this exercise is to replicate the payoff of the Secured Barrier Call by a linear combination of the known products: European up-out call (cost 12), digital strike 33 (cost 0.73) and ...
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### How to derive the relationship between log yield and log price?

This is a misnomer by Cochrane and Piazzesi. It should simply be called the continuously compounded yield.
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### Black Scholes in Practice: Delta Hedging

The $\Delta$ just define the time difference you are considering. In order to formulate the differential equation correctly you need to send $\Delta$ to zero. i.e $lim_\Delta\rightarrow 0$ In order ...
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1 vote
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1 vote
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### Which are the practical implications that the continuously compounded rate of return can be smaller than the expected rate of return?

The key word in your question is compounded. The expected arithmetic return for each $\Delta t$ is $\mu$, but the growth rate is $\mu - \frac{\sigma^2}{2}$. As others mentioned, volatility reduces ...
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### Can anyone explain to how Hull get from stock returns to continuously compounded stock returns?

The key is on the left hand side. Recall that the differential of log of x is: $d \ln x =\frac{1}{x}dx$ So you get: $\ln x_t-\ln x_0=at$ Which you will need to exponentiate to get rid of the log: ...
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The first result you are alluding to is known as the martingale representation theorem. More specifically, what you say holds for continuous paths processes. For jump processes, there can and will a $... • 14.7k 1 vote ### Bjork exercise 7.6: Claim that depends on$T_1$and$T_0$The spot price process is driven by a constant coefficient geometric Brownian motion. Thus, the ratio$S \left( T_1 \right) / S \left( T_0 \right)$is independent of$\mathcal{F} \left( T_0 \right)\$ ...
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