Geon Ho Choe

Abstract We propose a new method of measuring the third and fourth moments of return distribution based on quadratic variation method when the return process is assumed to have zero drift. The realized third and fourth moment variations computed from high‐frequency return series are good approximations to corresponding actual moments of the return distribution. An investor holding an asset with skewed or fat‐tailed distribution is able to hedge the tail risk by contracting the third or fourth mo

Let $0 < \theta < 1$ be irrational and $T_{\theta} x = x + \theta \bmod 1$ on $[0,1)$. Consider the partition $\mathcal{Q}_n = \{[(i - 1) / 2^n, i/2^n) : 1 \leq i \leq 2^n\}$ and let $Q_n(x)$ denote the interval in $\mathcal{Q}_n$ containing $x$. Define two versions of the first return time: $J_n(x) = \min\{ j \geq 1 : \| x - {T_{\theta}}^j x \| = \| j \cdot \theta \| < 1/2^n \}$ where $\| t \| = \min_{n \in \mathbf{Z}} |t - n|$, and $K_n(x) = \min\{ j \geq 1 : {T_\theta}^j x \in Q_n(x) \}$. We

A point x in [0,1] is represented as a binary expansion, i.e. it is identified with an infinite binary sequence of 0 and 1. Given a map T satisfying 0⩽T(x)⩽1 for 0⩽x⩽1, we iterate the map T until the first n bits in x recur as the first n bits in the Knth iterate TKn(x) for some Kn = Kn(x). We call Kn(x) the nth recurrence time of x. More precisely, put En,j = [ (j−1)/2n,j/2n), 1⩽j⩽2n, and let En(x) be one of the intervals En,j containing x. Then Kn(x) = min{j⩾1:Tj(x)∊En(x)}. For higher dimensio

We investigate the spectral types of unitary operator <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper U"> <mml:semantics> <mml:mi>U</mml:mi> <mml:annotation encoding="application/x-tex">U</mml:annotation> </mml:semantics> </mml:math> </inline-formula> on <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper L squared left-parenthesis double-struck upper T right-parent

We propose an alternative method for finding the kth default time distribution in a homogeneous portfolio with dependency. Analysing order statistics of default times with a one-factor Gaussian copula model, we explicitly derive the probability distribution. Moreover, we compute the prices of basket default swaps such as the kth to default swaps and m out of n default swaps within our framework. To test the efficiency and accuracy of our method we compare the theoretical prediction with existing

Abstract We present closed‐form lower bounds for the price of arithmetic average Asian options under geometric Brownian motion. Lower bounds are found by conditioning on multiple normal variables, each of which is a weighted sum of Brownian motions. Numerical results show that our lower bounds are close to Monte Carlo prices and improve single conditioning methods especially for high volatility and long maturity.