# All Questions

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### How do you optimize an all equity portfolio while getting around the multicollinearity issue?

I am trying to optimize a portfolio of domestic and international equity funds. However being that they are very highly correlated it doesn’t really help. Is there a way to optimize and find an ...
25 views

### Swap curve is unsmooth at front end with naive interpolation

I am looking at swap curve building at front end and find it difficult to get a smooth forward curve with a fast generic algorithm. For example, EUR 6m curve has 6m deposit, and then a series of FRAs (...
13 views

### American ImpVol Surface w/ DIVs - Is there any method that works in 2020?

Goal is simply to retrieve, from market quote data, the Implied volatility smiles and vol surface for American Options on US Equities (Calls & PUTS). Have not found a reliable way to do this, this ...
63 views

### Difference between OIS Rate and Risk-Free Rate

What exactly is the difference between the fixed rate of an OIS and the risk-free rate in that currency. For example, in the US the OIS rate vs. risk-free rate SOFR or in the UK the OIS rate vs. the ...
53 views

### Is the volatility smile a thing of the past?

Looking for example at this image from bloomberg of the OMX volatility surface, there is only a faint resemble of a smile at the shortest tenors that quickly dissipates as maturity is increased. I ...
77 views

### Impact of fixing on the valuation of derivatives

I would like to know what is the impact of a fixing on the value of a fixed vs floating interest rate swap (IRS). Also, I have the same question about the fixing impact on a cross currency swap? On a ...
47 views

### Silly question: Why don't traders look at the sqrt(Var[ABC] - Var[XYZ]) when looking at gaps?

As you know, variances are additive but volatilities are not. If that is the case and I open a long position on product ABC at an implied vol of 28% and a short position on product XYZ at an implied ...
30 views

### How to get commodity futures settlement timepoints?

I need to find some easy approach to get the daily settlement times (not the exact milisecond, just the general rule hh:mm) for multiple commodity futures (agriculture, metals, energy) on multiple ...
29 views

### Getting real-time stock market data in one file

There are lots of services which provide stock market data on ticket-by-ticker basis, so to get the 1-min data for each US stock I will need to perform a few thousand requests each minute. Is there ...
34 views

### How does a volatility surface based on moneyness instead of strike stay consistent with put-call parity?

By definition due to put-call parity the implied volatility will be the same for puts and calls with the same strike price and time to maturity. Meanwhile, a volatility surface is often quoted in ...
13 views

### Applying GARCH to Panel Data

I have a panel consisting of some quantity - say earnings/cash flows/or something similar. I am interested in forecasting the volatility that is inherent to that respective measure. In a single time ...
33 views

### Explicit expression for option prices in SABR?

I am trying to get a grip of the current state of research regarding option pricing in the SABR model. Am I correct in that, so far, there is no known general formula for the option price in the SABR ...
31 views

### How does Bloomberg calculate beta?

I tried manually calculating Bloomberg's historical beta based on the historical spread of SPY and equity price data, but I couldn't get the same result. I read somewhere that Bloomberg's default ...
216 views

### Impact on DV01 of cbot bond futures by changing coupon from 6% to 4%

CBOT has been asking customers lately what their thoughts would be on coupon change from 6% to 4% on all bond futures. I believe the last time this was done was in 2000 where the coupon was changed ...
28 views

### 15-min, 30-min and 60-min volatility forecasts

I have high-frequency market data (irregularly spaced nanosecond timestamps) and would like to compute the volatility forecasts of the next 15, 30 and 60 minutes. Most of the literature I looked up ...
25 views

### Quantlib Yield Curve given spot and forward rate

Is it possible to create a yield curve, given the spot rate and the forward rate?
42 views

### Determining the early exercise curve of an American option

When I have found the price of an American option using, say, a finite difference scheme - how do I find the early exercise curve from this solution? Here is my idea: What I have is the price of the ...
54 views

### Transition to SOFR Swaps and single curve pricing

As in the US there is a push to replace IBOR based swaps with SOFR rate does that mean that SOFR swap pricing will return to using a single curve framework as LIBOR swaps did pre the financial crisis?
66 views

### Derivation of $u=e^{\sigma\sqrt{dt}}$ and $d=e^{-\sigma\sqrt{dt}}$

Anyone could provide me a proof of how, starting from $\frac{dS_T}{S_t}\sim \operatorname{N}(\mu dt,\sigma^2 dt)$ with $p:=\frac{e^{rdt}-d}{u-d}$, we can obtain the parameters $u$ and $d$ as from ...
80 views

### Derivation of the Sharpe ratio [closed]

How to derive the Sharpe ratio of a portfolio? Is it different or similar to the CAPM derivation of the Sharpe ratio? How to reconcile the two derivations Line by line, plus official sources would be ...
65 views

### How can the increments of a CIR process be derived?

For a CIR process, which has SDE $$dr_t = \alpha (\mu - r_t) dt + \sigma \sqrt{r_t} dW_t$$ how can I derive the increments over the discrete time-interval from $r_t$ to $r_{t+1}$?
39 views

### Replicating portfolio

I have a doubt about the replicating portfolio methodology. Example - Consider an European Call with $K=21$ and underlying with current price $S_0=20$. We assume that, at the maturity, the underlying ...
72 views

### Relationship between Beta and implied volatility

Is there any way to make use of the Beta of an underlying and index, and the implied volatility of options on that underlying and the index? To specify, if we have available the implied volatility of ...
37 views

### How to apply Kalman Filter to GDP data?

Once reverted the Merton/Vasicek formula I could compute the $PD^{PIT}$ for IFRS9 as $PD^{PIT}_i(z) = \Phi \left( \phi^{-1}(PD^{TTC}_i) \sqrt{1-\rho_i} + \sqrt{\rho_i}z\right)$ The main issue is to ...
77 views

### Bond prices and probability of default

We learn in Finance 101 that the price of a bond is the present value of future cash flows. There is no mention of default risk. Still, bond prices move each day, without a change in the payment ...
38 views

### Pegged Orders Positioning

I have a strategy that involves being first in the order queue in a tight market where the tick can change from bid to ask or ask to bid by one tick. I am looking at pegged orders so when the bid ...
92 views

### Objective probability of default from CDS spread

I have the risk neutral probability of default extrapolated from the market data of the CDS spreads. How can I empirically estimate the market risk price of the objective probability of default (i.e. ...
33 views

### Poisson modelling of non-life insurance claims with reporting delay

I am considering a portfolio of car insurance policies. In order to capture the individual history (driving skills, age, etc.) of policyholders, it is assumed that the claim numbers $N(t)$ are modeled ...
35 views

### CME Metals Settlement methodology

I'm reading the docs on CME Metal's settlement methodology and looking at the examples section: https://www.cmegroup.com/confluence/display/EPICSANDBOX/Metals+Futures+Settlement+Algorithm+Examples For ...
48 views

### Inflation Option Modelling Approaches

I am trying to come up with a simplistic inflation option model to get a sense of the materiality of some inflation-indexed contracts containing inflation guarantees. I have a stochastic nominal IR ...
31 views

### Hypothesis regarding a recursive annuity loan

I have a question regarding an annuity loan calculation and I would like to prove whether the hypothesis I am stating is correct: Consider an annuity loan $L_{1}$, with a principal of $T_{1} = 100$ ...
27 views

### Mismatch of periods with numeraire compared to the forward rates

In Joshi's The Concepts and Practice of Mathematical Finance Page 323--324 I believe that there may be a mismatch of periods with forward rates: Consider time partition $t_{0} < ... < t_{n}$ ...
80 views

### VaR and Expected Shortfall for Geometric Brownian Motion

Given that $dS_t=\mu S_tdt+\sigma S_tdW_t$ ,a risk free rate r and defining Value at Risk and Expected Shortfall as $VaR_{t,a}=S_0e^{rt}-x$ where $x$ is the amount such that $P(S_t\leq x)=1-a$ ($a:$...
54 views

41 views

### Determining Presence of Arbitrage

I am slightly confused by part (b) of this question. My understanding is that the easiest way to determine if there is arbitrage is to compute the state prices and then look at their sign: if one or ...
33 views

### Cross-listed stocks - how to get capital allocation per country?

https://en.wikipedia.org/wiki/Cross_listing Cross-listing (or multi-listing, or interlisting) of shares is when a firm lists its equity shares on one or more foreign stock exchange in addition to its ...
36 views

### finding log returns for multiple stocks using R [closed]

Consider a portfolio with four stocks Google(GOOG), 3M(MMM), Microsoft (MSFT), and IBM(IBM). We are interested in monthly return (log return between 22 business days) of the portfolio elements from 01/...
24 views

### Yahoo finance continuous futures historical data

How is Yahoo Finance's continuous futures historical data calculated? Are these front-month numbers?
667 views

### Option Price vs. Implied Volatility

I was doing an exercise on investigating the relationship between European Call option price and its volatility. I was asked to compute $\frac{\partial^2C}{\partial \sigma^2}$ and find out the domain ...