# Is TVOG equal to the cost of guarantees mathematically?

Discussion in 'SP2' started by Michael Lee, Jul 3, 2021.

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1. ### Michael LeeMade first post

As we know, the TVOG is the time value of the options and guarantees, and the calculation is the difference between the average CE(current estimate) under 1000 stochastic scenarios and the CE

The Cost of guarantees is the average number of sum of PV max(guaranteed benefits(t) - Asset share(t),0) under 1000 stochastic scenarios.

From principle, the TVOG is likely to be equal to the Cost of guarantees, but is the TVOG equal to the cost of guarantees mathematically?

2. ### mugonoTon up Member

The value of an option is equal to the intrinsic value + time value.

The cost of guarantees is equal to TVOG if the contract is ‘out of the money’ (ie intrinsic value = 0).

3. ### Michael LeeMade first post

There will be the scenario that ‘out of the money’ and ‘in the money’ under 1000 stochastic scenario,and both TVOG and cost of guarantee take 1000sims into consideration, so i am confused about the ‘The cost of guarantees is equal to TVOG if the contract is ‘out of the money’’

4. ### mugonoTon up Member

Example: a with profit contract may have a guarantee that exceeds the asset share. The difference between the guarantee and asset share is the ‘in the money’ component of the overall cost to the insurance company. The stochastic simulations will project the cash flows over the maturity of the contract. In some scenarios, the position will reverse (ie asset share > guarantees) and in other scenarios it will not. The average of all results will give you the TVOG.

5. ### Michael LeeMade first post

Thanks for your kindly response, so the cost of guarantee is equal to the TVOG from principle, but how to prove it mathematically?

6. ### mugonoTon up Member

The TVOG can be valued using option pricing techniques. CM2 may set out what you’re looking for.