9

There are "perpetual" bonds and preferred shares that are traded in the corporate credit markets that exactly match your conditions above. They are recorded in the 10-K at notional value $X$. The "close-out" feature is an embedded call. You should assume your favorite stochastic interest rate (and/or credit) model and run a PDE solver, tree, or other grid ...


9

Why does USD based security valuation have to give a thing about what London Banks think? Your question is based on false premises: the USD Libor is not determined by polling London based banks as you seem to believe, but banks on the London money market. The difference is important, as there are—of course—banks which are not based in London and active on ...


9

A swaption in which the underlying swap starts at a date materially after the expiration date is called a midcurve swaption. The implied volatilities of these can not be obtained from the regular swaption surface. Market makers calculate implied volatilities for midcurves in s number of ways. One popular method is to compute the volatility of the forward ...


7

We actually managed to come up with the answer to this question ourselves but wanted to share the answer since it might be relevant to others as well. The calculation depends on what method is used to calculate the cost. There is the FIFO, LIFO and the average cost method, see: http://www.accounting-basics-for-students.com/fifo-method.html If FIFO or LIFO ...


7

If you imagine you have two risk-less assets that have a unit payoff at maturity $V_1(T) = V_2(T) = 1$ but their present value is not equal, e.g. $V_1(t) < V_2(t)$. You buy the cheaper, sell the more expensive, have a strictly positive cash-flow today and at maturity the cash-flows cancel out with certainty. This is a free lunch arbitrage. The same ...


6

You are essentially dealing with two options: $EU\,{Warrant}(S_t) = BlackScholesCall(S_t)+CompoundCall(S_t)$ The Black-Scholes formula is known, and Compound Option pricing has various approaches in research which you may find.


6

You should use the full yield curve, discounting cash flows at specific dates using the appropriate zero-coupon interest rate. As to which yield curve, that is often a matter of convention. Generally one uses the LIBOR/swaps curve for all but the most liquid products (in which case you use the treasury curve). The curve is constructed from LIBOR/Eurodollar ...


6

To discuss Funding Valuation Adjustments (FVA) it is first necessary to describe a situation in which such an adjustment would be needed. In here we will take as an example collateral mismatches, which is a common case. For a conceptual treatment of FVA and collateral mismatches refer to Ruiz (2013). We borrow the modified Black-Scholes framework of ...


5

You will find elaborate answers to your question in this excellent new book: Quantitative Value: A Practitioner’s Guide to Automating Intelligent Investment and Eliminating Behavioral Errors by Gray & Carlisle You can find a good summary over at CXO Advisory Group: A Few Notes on Quantitative Value


5

If you assume that you do not have any market risk (a strange assumption, but it would hold for example if you are fully hedged), then a (correctly) collaterlized derivative does not have any net future cash flow. Clearly: if the derivative contract has a cash flow of -X, its value will go down by X and the collateral account will have a cash flow of +X (the ...


5

The importance here is that it actually does not matter in what time zone or market the libor rates are set. Key is that it is supposed (!!!) to be a gauge at what rate contributing banks could borrow funds at in the inter-bank market. Like you can go to any African country and borrow or lend US dollar, so can any Japanese, European, or American bank borrow ...


5

In #2, you can use FX forwards to convert your JPY cashflows to USD but it is more common in practice to use a cross-currency swap for this purpose. Indeed, the advantage of the latter is that it allows you to keep the nominal of your synthetic USD bond constant because the final exchange in the swap is done at FX spot (not forward), and the difference is ...


5

Trading bond futures calendar spread is actually a very involved exercise, with many moving parts. But first things first, recall that bond futures price is approximately: $$ F = \text{spot price} - \text{carry} - \text{delivery option value (DOV)} \pm \text{rich/cheap}.$$ So calendar spreads represent the differences in spot prices, in carries, in delivery ...


4

Just figured it out with the help from someone else... The market cap is in Singapore dollar because it's traded on Singapore exchange, but their income statement is in Thai Baht... That's why :)


3

Depends on circumstances - if you just trade futures intraday for yourself, secondary market T-bills (http://www.federalreserve.gov/releases/h15/data.htm#fn3) will be good enough.


3

A condition for correct calibration of the short rate model is that it exactly reproduce the present values of fixed (option-free) cashflows - that is, that it give the same answer as ordinary discounting at the spot rate. If it doesn't, you've done something wrong - sort of like using a model that violates put-call parity. (Actually, it's exactly like that.)...


3

As long as your market is complete and $\tau$ is measurable w.r.t. the filtration generated by the market the continuous cash flow paid until $\tau$ is a hedgeable contingent claim and you have to work under the risk neutral measure.


3

Basically it boils down to this: You either use a descriptive or a prescriptive (normative) model, i.e. you either think that the market is always right or you think that you alone know how to determine the "true" price of an option. The original idea of BS was to build a prescriptive model but most modern models try to take the market prices as given and ...


3

Bank earnings specifically, but yes. http://www.macrotrends.net/1324/s-p-500-earnings-history


3

There are papers out there applying this approach. Try looking up Leland, Leland&Toft (1994 and 1996) for modelling corporate liabilities, resulting in a series of interesting results. Also, it might be worth looking into a structural credit risk modelling approach (in contrast to a reduced form approach (see Lando (2001 or 2004) for more)). There are ...


3

A dollar to be received with certainty (for example, you have purchased a bill from the US government) at time $t$ will be valued at $e^{-rt}$. If you are uncertain about whether you will receive the dollar or not, you should take this into account. A simple model is that the institution who is supposed to pay you will default with probability $p$, in which ...


3

I performed spectral analysis on the stock market for disaggregated returns. If $\mu$ is the center of location and anything away from $\mu$ is an "error", then the stock market is in equilibrium once every 20-21 years as an aggregate whole. But, like a musical instrument, the periods of the individual firms could be relatively small. Still, that would ...


3

If you already have the zero rates, you can construct the zero curve using the set of maturities (dates) and zero rates values, in addition to a day count convention in this way: import QuantLib as ql ql.Settings.instance().evaluationDate = ql.Date(26, 7, 2018) dates = [ql.Date(26, 7, 2019), ql.Date(26, 7, 2020), ql.Date(26, 7, 2030)] zero_rates = [0.03, 0....


3

Sums the market value times the par value for each bond Could you clarify that formula ? From what you wrote it seems to be just a way to dollarize the bond price (market value = 97%, par value = 200 000 USD, bond value(market price) = 194 000 USD) Par value weighted average is a very poor metric of measuring (short term) portfolio risk. It is however ...


3

Based on an my updated understanding of your problem you have a portfolio consisting of $N$ illiquid assets. Valuations are not real time and usually lagged, by say, upto 3 months (or slightly longer), but at least valuations correspond to a consistent timestamp (or otherwise you interpolate a consistent timestamp). You want to construct a predictive model ...


3

@Gordon has already given the answer but here is a little more notes to it... At time time $T_2$ the holder receives $X=(S_{T_1}-K)^+$. According to Risk Neutral Valuation the value at time $t$ $(t<T_1<T_2)$ is $$V_t = e^{-r(T_2-t)}E_t[(S_{T_1}-K)^+] = \\ e^{-r(T_2-t+T_1-T_1)}E_t[(S_{T_1}-K)^+]=\\ e^{-r(T_2-T_1)}e^{-r(T_1-t)}E_t[(S_{T_1}-K)^+] $$ $e^...


2

I think the formula you refer to is $$ PV=\frac{C}{r-g} $$ If that's the case, then you do not subtract growth, the minus sign has an advantage on the present value. The initial formula $PV=\frac{C}{r}$ assumes no evolution in $C$, but the other one assumes the that the payment will grow in time hence yes, you get paid for that.


2

Alright, here's the proof (I think): Statement of APT: $$E(r_a)=r_f + \displaystyle\sum_{i=1}^n\lambda_i * cov(r_a, r_i)$$ Expand $E(r_a)$: $$\frac{E(C_1)}{PV_0} - 1 =r_f + \displaystyle\sum_{i=1}^n\lambda_i * cov(\frac{C_1}{PV_0} - 1, r_i)$$ Since $PV_0$ doesn't have any covariance with $r_i$, we can reduce the above to the following: $$\frac{E(C_1)}{...


2

Mortgage backed securities are valued by calculating the net present value (NPV) of cash flows they are expected to generate. These cash flows are predicted using a model that incorporates all the contractual characteristics of the security and the underlying loans, as well as assumptions on things like prepayment speed, default speed, loss severity, and ...


2

Nearly every options trader - and every options marketmaker - will hedge their derivatives exposure by trading the underlying. So even if I buy a set of naked calls, my counterparty (e.g. whoever is writing me the options, usually a hedge fund or a bank) will have negative exposure to the stock and buy it to cancel out their risk. Think of an option as ...


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