Would anyone know what does it mean to value an asset in "forward space" versus "zero space" ? where does one start from when trying to dig into the meaning of this? Thanks in advance.
In interest rate land you can look at the yield curve in 3 ways: par space (a chart of the par swap rates of different maturities) , zero space (the zero coupon swap rates) and forward space (usually the 3 month forward rates for various maturities). These are equivalent ways to display the prevailing market rates. Perhaps that is what is being referred to
This sounds to me like an unclear reference to the difference between the spot risk-neutral measure ('zero' curves relate to rates starting today which is generally called 'spot') and the forward measure.
These are different ways to formulate the pricing of derivative securities. They use different numeraires (the idea is that an asset known as the numeraire is the basic unit of currency). Using different measures can allow us to greatly simplify a pricing formula and obtain a closed-form expression.