# Tag Info

5

While another user touched on the hedging argument in order to reconcile your intuition with the correct value of the option he went off track (imho). I like to focus entirely on the hedging issue because it is key in understanding the differences in intuition and the fair price of such option. Unfortunately I have hardly ever found a simple 1-2 paragraph ...

3

Constructing the right supermartingale is the key step. Consider the process $$X_t := \underset{Q \in \mathbb{P}}{\text{esssup}} \ E_Q \left[ H | \mathcal{F}_t \right].$$ This process $X$ is well-defined, since $\underset{Q \in \mathbb{P}}{\sup} E_Q [H] < \infty$. One can show that $X_t$ is a supermartingale under every $Q$ in $\mathbb{P}$. This ...

3

You are treading controversial waters. It's hard to summarize, but at the risk of oversimplifying, there are three broad schools of thought: "Linear Models": Classic Examples are a string of papers from Jasmina Hasanhodzic and Andy Lo at MIT (scholar.google.com should give you plenty). For similar work related to Mutual Funds that you may be able to ...

2

When performing a tracking error optimization, you will obtain the same result by using the tracking error squared, which is just the variance of the relative portfolio weights. This would be just finding the minimum variance portfolio, but with conditions on the weights. For instance, it would be equivalent to instead set up the variance minimization ...

1

these kinds of questions usually require careful attention to details: if it's a hw question of some kind, consult shreve's lecture notes, he has a whole section on this precise topic in all its glory. as for intuition, since holding $\frac{\partial \xi}{\partial S}$ at any point in time eliminates the dW term, in the context of a discrete time period model ...

1

It is better to use a factor model, if one is available. Are you asking this question because you don't have access to one? Also, what is the nature of the asset you want to track? Is it an index or a single security? What asset class? What risk factors is it exposed to (e.g. interest rate and credit risk vs. stock market volatility and other equity ...

1

definition of a variance swap is $\int^{T+\Delta}_T \mathbb{E}_t[v_s] ds$ where $v_s$ is the variance and $\mathbb{E}_t[v_s]$ is the expectation of the variance of time s at time t. therefore, pnl is: $(\int^{T+\Delta}_T \mathbb{E}_t[v_s] ds - \int^{T+\Delta}_{T} \mathbb{E}_{t-\delta}[v_s] ds)*d\delta$

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