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We consider the forward value, which can be employed to estimate the equity value. Let $T_1=0.5$ be the dividend payment time, and $T=1$. Moreover, let $r_1=5\,\%$ be the annualized interest rate to $T_1$, $r=6\,\%$ be the interest rate to $T$, and $d=5$ be the dividend payment. Then, the forward value, under the risk-neutral measure with the deterministic ...


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The relationship between interest rates and equity prices being at best unstable and weak, I'll assume that the level of interest rate is irrelevant here. So the answer to your question (price of the equity in a year) is 95, everything else being equal. Of course it's unlikely that the equity will actually price at 95 in a year due to market movements, but ...


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According to money market expert Scott Skyrm: quote The FRRP provides a floor to the market because as overnight rates approach the FRRP rate, more volume is executed at the facility and more collateral is added to the market, removing cash. The IOER acts as a ceiling in the overnight market by adding cash, though indirectly. When market rates like fed ...


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You're writing it in terms of the growth factors and annual compounding. You want to split up $M$ so that as each piece grows over time, the $i$th person at time $n_i$ gets paid the same amount as the $j$th person gets at time $n_j$. So simply scale by the corresponding discount factors. Let $$ \alpha_i = \frac{(1+r)^{-n_i}}{\sum_j (1+r)^{-n_j}} $$ Then ...


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in the context of bonds / fixed income an annuity is a payment which is made at regular time intervals - a cupon. A continuous one is simply being paid for an unlimited amount of time. PV = Cupon/ (1+r)^1 + ...... Cupon/ (1+r)^t just to add to Bob's comment above, a "continuously compounding" annuity is re-invested at the same rate every month on top of ...


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Yes you can! Any SDE that has an analytic solution can be simulated exactly. The vasicek model has dynamics $dr=a(b-r)dt+\sigma dW_t$. By Ito's lemma, $$d\left(e^{at}r\right)=e^{at}\left(a(b-r)dt+\sigma dW_t\right) +a e^{at} r dt$$ Simplifying, $$d\left(e^{at}r\right)=e^{at} ab +e^{at}\sigma dW_t$$ Integrating, $$e^{aT} r_T=r_0+b(e^{aT}-1)+\sigma \int_0 ...



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