Skip to main content
Quantitative Finance

Return to Question

added 1 character in body
Source Link
Richi Wa
Richi Wa
  • 13.8k
  • 6
  • 41
  • 91

Let $$ X_t = \mu t + \sigma B_t $$ be a linear Brownian motion with drift. Let $$ S_t = \max(X_u, u \le t) $$ denote the process of allthe running max, then the draw down is given by $$ DD_t = S_t - X_t $$$$ DD_t = S_t - X_t, $$ and the maximum draw down over a period $[0,T]$ is $$max_{u \in [0,T]} DD_u.$$ What can we say about $$E[ max_{u \in [0,T]} DD_u ] ?$$ How can we calculate the expected maximum draw down? Are there analytical formulas, approximations, available (R) packages?

Let $$ X_t = \mu t + \sigma B_t $$ be a linear Brownian motion with drift. Let $$ S_t = \max(X_u, u \le t) $$ denote the process of all running max, then the draw down is given by $$ DD_t = S_t - X_t $$ and the maximum draw down over a period $[0,T]$ is $$max_{u \in [0,T]} DD_u.$$ What can we say about $$E[ max_{u \in [0,T]} DD_u ] ?$$ How can we calculate the expected maximum draw down? Are there analytical formulas, approximations, available (R) packages?

Let $$ X_t = \mu t + \sigma B_t $$ be a linear Brownian motion with drift. Let $$ S_t = \max(X_u, u \le t) $$ denote the process of the running max, then the draw down is given by $$ DD_t = S_t - X_t, $$ and the maximum draw down over a period $[0,T]$ is $$max_{u \in [0,T]} DD_u.$$ What can we say about $$E[ max_{u \in [0,T]} DD_u ] ?$$ How can we calculate the expected maximum draw down? Are there analytical formulas, approximations, available (R) packages?

Tweeted twitter.com/#!/StackQuant/status/593621491775840257
Source Link
Richi Wa
Richi Wa
  • 13.8k
  • 6
  • 41
  • 91

Expectation of maximum draw down in the Brownian motion case

Let $$ X_t = \mu t + \sigma B_t $$ be a linear Brownian motion with drift. Let $$ S_t = \max(X_u, u \le t) $$ denote the process of all running max, then the draw down is given by $$ DD_t = S_t - X_t $$ and the maximum draw down over a period $[0,T]$ is $$max_{u \in [0,T]} DD_u.$$ What can we say about $$E[ max_{u \in [0,T]} DD_u ] ?$$ How can we calculate the expected maximum draw down? Are there analytical formulas, approximations, available (R) packages?