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1

Let $(B_t)$ be a standard Brownian motion. Then, $B_t\sim N(0,t)$ and $B_t-B_s\sim N(0,t-s)$. Informally, you can say $\mathrm{d}B_t\sim N(0,\mathrm{d}t)$ where $\mathrm{d}B_t=B_{t+\mathrm{d}t}-B_t$ is an infinitesimal increment.


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In any "arbitrage" situation, you are trying to create a scenario where you sold a rich asset and bought a cheap asset, while keeping the overall position as flat as possible to risk. Assuming interest rates have not changed from continuously compounded 4%, and the company can borrow at this rate and sell a forward at this rate. The company is buying the ...


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This is kinda 'super-replication'. You want to find the minimum amount $w$ that you need to invest such that a portfolio of $x$ amount of bank account and $y$ units of the stock, which costs less than $w$ initially and which you can dynamically adjust subject to no new injection of money ($x_{n-} + y_{n−}S_n ≥ x_n + y_nS_n$), returns at least the option ...


2

Already answered, but... from scipy.optimize import root def pv(r): return 2000 / (1+r)**2 + 3000 / (1+r)**4 rate = root(lambda x: pv(x) - 4000, 0.)['x'][0] print(f"Rate is {rate*100:.5f}%") print(f"Present Value is {pv(rate):,.2f}") Rate is 7.30274% Present Value is 4,000.00


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try this : 4000= 2000/(1+r)^2 + 3000/(1+r)^4 solving this equation for r you'll find equals 7.30274083178438%.


2

I start with some general information and answer your questions below. I'll assume continuous compounding. The bond price is given by \begin{align*} P_B=\sum_{i=1}^n c_{t_i} \cdot e^{-y\cdot t_i}, \end{align*} where $c_{t_i}$ denote the $n$ coupon payments occurring at time points $t_i$ and $y$ the yield-to-maturity. Note that the last payment $c_{t_n}$ ...


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Annual Accounting Profit = Revenues -costs - depreciation Revenues =13000 Costs= 10000 Annual depreciation = 30000/10yrs = 3000 Therefore annual accounting profit =0 If you believe that the property market value will indeed depreciate like this, it doesn’t seem like a good investment.


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Assume the put option with strike 45 is worth 8 and the put option with 40 is trading at 5. For the bull spread, you sell the 45 strike option and buy the 40 strike option. So your payoff and profit will look as follows (profit=payoff+net premium): Instead if you sell 10 options of strike 45 and buy 10 options of the other strike, profit graph will just ...


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